Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits

Let p , b ≥ 2 be two integers, and let D = p...
Ausführliche Beschreibung

Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , … , b − 1 } . It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d ( x ) = ( p b ) − 1 ( x + d ) } d ∈ D is a spectral measure with a spectrum Λ ( p b , C ) = ∑ j = 0 finite ( p b ) j c j : c j ∈ C = { 0 , 1 , … , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , … , t r such that the scaling set ∏ i = 1 r t i k i Λ ( p b , C ) is also a spectrum of μ p b , D for all k i ≥ 0 . Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Chi, Zi-Chao [verfasserIn] Li, Qian [verfasserIn] Lv, Jun [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Self-similar measure Primitive Spectral eigenvalue problems Consecutive digits

Übergeordnetes Werk:	Enthalten in: Chaos, solitons & fractals - Amsterdam [u.a.] : Elsevier Science, 1991, 173
Übergeordnetes Werk:	volume:173

DOI / URN:	10.1016/j.chaos.2023.113648

Katalog-ID:	ELV060483954

Internformat


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245	1	0	\|a Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits
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520			\|a Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , … , b − 1 } . It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d ( x ) = ( p b ) − 1 ( x + d ) } d ∈ D is a spectral measure with a spectrum Λ ( p b , C ) = ∑ j = 0 finite ( p b ) j c j : c j ∈ C = { 0 , 1 , … , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , … , t r such that the scaling set ∏ i = 1 r t i k i Λ ( p b , C ) is also a spectrum of μ p b , D for all k i ≥ 0 .
650		4	\|a Self-similar measure
650		4	\|a Primitive
650		4	\|a Spectral eigenvalue problems
650		4	\|a Consecutive digits
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700	1		\|a Lv, Jun \|e verfasserin \|4 aut
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912			\|a GBV_ILN_2027
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912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
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allfields	10.1016/j.chaos.2023.113648 doi (DE-627)ELV060483954 (ELSEVIER)S0960-0779(23)00549-0 DE-627 ger DE-627 rda eng 510 VZ 30.20 bkl 31.00 bkl Chi, Zi-Chao verfasserin aut Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , … , b − 1 } . It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d ( x ) = ( p b ) − 1 ( x + d ) } d ∈ D is a spectral measure with a spectrum Λ ( p b , C ) = ∑ j = 0 finite ( p b ) j c j : c j ∈ C = { 0 , 1 , … , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , … , t r such that the scaling set ∏ i = 1 r t i k i Λ ( p b , C ) is also a spectrum of μ p b , D for all k i ≥ 0 . Self-similar measure Primitive Spectral eigenvalue problems Consecutive digits Li, Qian verfasserin aut Lv, Jun verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 173 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:173 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 30.20 Nichtlineare Dynamik VZ 31.00 Mathematik: Allgemeines VZ AR 173
spelling	10.1016/j.chaos.2023.113648 doi (DE-627)ELV060483954 (ELSEVIER)S0960-0779(23)00549-0 DE-627 ger DE-627 rda eng 510 VZ 30.20 bkl 31.00 bkl Chi, Zi-Chao verfasserin aut Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , … , b − 1 } . It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d ( x ) = ( p b ) − 1 ( x + d ) } d ∈ D is a spectral measure with a spectrum Λ ( p b , C ) = ∑ j = 0 finite ( p b ) j c j : c j ∈ C = { 0 , 1 , … , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , … , t r such that the scaling set ∏ i = 1 r t i k i Λ ( p b , C ) is also a spectrum of μ p b , D for all k i ≥ 0 . Self-similar measure Primitive Spectral eigenvalue problems Consecutive digits Li, Qian verfasserin aut Lv, Jun verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 173 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:173 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 30.20 Nichtlineare Dynamik VZ 31.00 Mathematik: Allgemeines VZ AR 173
allfields_unstemmed	10.1016/j.chaos.2023.113648 doi (DE-627)ELV060483954 (ELSEVIER)S0960-0779(23)00549-0 DE-627 ger DE-627 rda eng 510 VZ 30.20 bkl 31.00 bkl Chi, Zi-Chao verfasserin aut Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , … , b − 1 } . It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d ( x ) = ( p b ) − 1 ( x + d ) } d ∈ D is a spectral measure with a spectrum Λ ( p b , C ) = ∑ j = 0 finite ( p b ) j c j : c j ∈ C = { 0 , 1 , … , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , … , t r such that the scaling set ∏ i = 1 r t i k i Λ ( p b , C ) is also a spectrum of μ p b , D for all k i ≥ 0 . Self-similar measure Primitive Spectral eigenvalue problems Consecutive digits Li, Qian verfasserin aut Lv, Jun verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 173 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:173 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 30.20 Nichtlineare Dynamik VZ 31.00 Mathematik: Allgemeines VZ AR 173
allfieldsGer	10.1016/j.chaos.2023.113648 doi (DE-627)ELV060483954 (ELSEVIER)S0960-0779(23)00549-0 DE-627 ger DE-627 rda eng 510 VZ 30.20 bkl 31.00 bkl Chi, Zi-Chao verfasserin aut Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , … , b − 1 } . It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d ( x ) = ( p b ) − 1 ( x + d ) } d ∈ D is a spectral measure with a spectrum Λ ( p b , C ) = ∑ j = 0 finite ( p b ) j c j : c j ∈ C = { 0 , 1 , … , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , … , t r such that the scaling set ∏ i = 1 r t i k i Λ ( p b , C ) is also a spectrum of μ p b , D for all k i ≥ 0 . Self-similar measure Primitive Spectral eigenvalue problems Consecutive digits Li, Qian verfasserin aut Lv, Jun verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 173 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:173 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 30.20 Nichtlineare Dynamik VZ 31.00 Mathematik: Allgemeines VZ AR 173
allfieldsSound	10.1016/j.chaos.2023.113648 doi (DE-627)ELV060483954 (ELSEVIER)S0960-0779(23)00549-0 DE-627 ger DE-627 rda eng 510 VZ 30.20 bkl 31.00 bkl Chi, Zi-Chao verfasserin aut Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , … , b − 1 } . It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d ( x ) = ( p b ) − 1 ( x + d ) } d ∈ D is a spectral measure with a spectrum Λ ( p b , C ) = ∑ j = 0 finite ( p b ) j c j : c j ∈ C = { 0 , 1 , … , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , … , t r such that the scaling set ∏ i = 1 r t i k i Λ ( p b , C ) is also a spectrum of μ p b , D for all k i ≥ 0 . Self-similar measure Primitive Spectral eigenvalue problems Consecutive digits Li, Qian verfasserin aut Lv, Jun verfasserin aut Enthalten in Chaos, solitons & fractals Amsterdam [u.a.] : Elsevier Science, 1991 173 Online-Ressource (DE-627)314118497 (DE-600)2003919-0 (DE-576)094504040 1873-2887 nnns volume:173 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 30.20 Nichtlineare Dynamik VZ 31.00 Mathematik: Allgemeines VZ AR 173
language	English
source	Enthalten in Chaos, solitons & fractals 173 volume:173
sourceStr	Enthalten in Chaos, solitons & fractals 173 volume:173
format_phy_str_mv	Article
bklname	Nichtlineare Dynamik Mathematik: Allgemeines
institution	findex.gbv.de
topic_facet	Self-similar measure Primitive Spectral eigenvalue problems Consecutive digits
dewey-raw	510
isfreeaccess_bool	false
container_title	Chaos, solitons & fractals
authorswithroles_txt_mv	Chi, Zi-Chao @@aut@@ Li, Qian @@aut@@ Lv, Jun @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	314118497
dewey-sort	3510
id	ELV060483954
language_de	englisch
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author	Chi, Zi-Chao
spellingShingle	Chi, Zi-Chao ddc 510 bkl 30.20 bkl 31.00 misc Self-similar measure misc Primitive misc Spectral eigenvalue problems misc Consecutive digits Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits
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topic_title	510 VZ 30.20 bkl 31.00 bkl Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits Self-similar measure Primitive Spectral eigenvalue problems Consecutive digits
topic	ddc 510 bkl 30.20 bkl 31.00 misc Self-similar measure misc Primitive misc Spectral eigenvalue problems misc Consecutive digits
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title	Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits
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title_full	Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits
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title_sort	number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits
title_auth	Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits
abstract	Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , … , b − 1 } . It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d ( x ) = ( p b ) − 1 ( x + d ) } d ∈ D is a spectral measure with a spectrum Λ ( p b , C ) = ∑ j = 0 finite ( p b ) j c j : c j ∈ C = { 0 , 1 , … , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , … , t r such that the scaling set ∏ i = 1 r t i k i Λ ( p b , C ) is also a spectrum of μ p b , D for all k i ≥ 0 .
abstractGer	Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , … , b − 1 } . It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d ( x ) = ( p b ) − 1 ( x + d ) } d ∈ D is a spectral measure with a spectrum Λ ( p b , C ) = ∑ j = 0 finite ( p b ) j c j : c j ∈ C = { 0 , 1 , … , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , … , t r such that the scaling set ∏ i = 1 r t i k i Λ ( p b , C ) is also a spectrum of μ p b , D for all k i ≥ 0 .
abstract_unstemmed	Let p , b ≥ 2 be two integers, and let D = p { 0 , 1 , … , b − 1 } . It is well known that the self-similar measure μ p b , D generated by the iterated function system { τ d ( x ) = ( p b ) − 1 ( x + d ) } d ∈ D is a spectral measure with a spectrum Λ ( p b , C ) = ∑ j = 0 finite ( p b ) j c j : c j ∈ C = { 0 , 1 , … , b − 1 } . In this paper, we study a class of primitive and composite numbers and their related properties. And we also explore the simple prime numbers and the properties related to their order. Based on these, let r be a positive integer, we give some conditions on the distinct prime numbers t 1 , t 2 , … , t r such that the scaling set ∏ i = 1 r t i k i Λ ( p b , C ) is also a spectrum of μ p b , D for all k i ≥ 0 .
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title_short	Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits
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Number theoretic considerations related to the scaling spectrum of self-similar measures with consecutive digits

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