On Uniform Truncation Error Bounds and Aliasing Error for Multidimensional Sampling Expansion
Abstract Let Bυ($ ℝ_{n} $), %$\silon = ({\silon _1},...,{\silon _n}) \in {\cal R}_ + ^n%$, be the set of entire functions of exponential type υ bounded on $ ℝ^{n} $ and %$B_{{p^\theta }}^r\left( {{{\cal R}^n}} \right),\,1 \leqslant p \leqslant \infty, 1 \leqslant \theta \leqslant \infty %$, be the a...
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| Autor*in: |
Jingfan, L. [verfasserIn] Gensun, F. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2003 |
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| Schlagwörter: |
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| Anmerkung: |
© SIP 2003 |
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| Übergeordnetes Werk: |
Enthalten in: Sampling theory, signal processing, and data analysis - [Cham] : Birkhäuser, 2021, 2(2003), 2 vom: 01. Mai, Seite 103-115 |
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| Übergeordnetes Werk: |
volume:2 ; year:2003 ; number:2 ; day:01 ; month:05 ; pages:103-115 |
| Links: |
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| DOI / URN: |
10.1007/BF03549388 |
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SPR043387233 |
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| 520 | |a Abstract Let Bυ($ ℝ_{n} $), %$\silon = ({\silon _1},...,{\silon _n}) \in {\cal R}_ + ^n%$, be the set of entire functions of exponential type υ bounded on $ ℝ^{n} $ and %$B_{{p^\theta }}^r\left( {{{\cal R}^n}} \right),\,1 \leqslant p \leqslant \infty, 1 \leqslant \theta \leqslant \infty %$, be the anisotropic Besov classes of functions. The uniform bounds of truncation error is estimated for f ∈ Bυ($ ℝ^{n} $) and satisfying the following decay condition:%${\left| {f(x)} \right| \leqslant \frac{A}{{(1 + {{\left| x \right|}^\delta })}},} \;\; {x = ({x_1},...,{x_n}) \in {{\cal R}^n},}%$associated with the Shannon multidimensional sampling representation. The bounds of aliasing error for %$f\, \in \,B_{{\infty ^\theta }}^r\left( {{{\cal R}^n}} \right)%$ and satisfying the same decay condition as above is also evaluated. | ||
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| 650 | 4 | |a anisotropic Besov class of functions |7 (dpeaa)DE-He213 | |
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10.1007/BF03549388 doi (DE-627)SPR043387233 (SPR)BF03549388-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 ASE Jingfan, L. verfasserin aut On Uniform Truncation Error Bounds and Aliasing Error for Multidimensional Sampling Expansion 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SIP 2003 Abstract Let Bυ($ ℝ_{n} $), %$\silon = ({\silon _1},...,{\silon _n}) \in {\cal R}_ + ^n%$, be the set of entire functions of exponential type υ bounded on $ ℝ^{n} $ and %$B_{{p^\theta }}^r\left( {{{\cal R}^n}} \right),\,1 \leqslant p \leqslant \infty, 1 \leqslant \theta \leqslant \infty %$, be the anisotropic Besov classes of functions. The uniform bounds of truncation error is estimated for f ∈ Bυ($ ℝ^{n} $) and satisfying the following decay condition:%${\left| {f(x)} \right| \leqslant \frac{A}{{(1 + {{\left| x \right|}^\delta })}},} \;\; {x = ({x_1},...,{x_n}) \in {{\cal R}^n},}%$associated with the Shannon multidimensional sampling representation. The bounds of aliasing error for %$f\, \in \,B_{{\infty ^\theta }}^r\left( {{{\cal R}^n}} \right)%$ and satisfying the same decay condition as above is also evaluated. Truncation error (dpeaa)DE-He213 aliasing error (dpeaa)DE-He213 band-limited function (dpeaa)DE-He213 anisotropic Besov class of functions (dpeaa)DE-He213 Gensun, F. verfasserin aut Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 2(2003), 2 vom: 01. Mai, Seite 103-115 (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:2 year:2003 number:2 day:01 month:05 pages:103-115 https://dx.doi.org/10.1007/BF03549388 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2 2003 2 01 05 103-115 |
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10.1007/BF03549388 doi (DE-627)SPR043387233 (SPR)BF03549388-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 ASE Jingfan, L. verfasserin aut On Uniform Truncation Error Bounds and Aliasing Error for Multidimensional Sampling Expansion 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SIP 2003 Abstract Let Bυ($ ℝ_{n} $), %$\silon = ({\silon _1},...,{\silon _n}) \in {\cal R}_ + ^n%$, be the set of entire functions of exponential type υ bounded on $ ℝ^{n} $ and %$B_{{p^\theta }}^r\left( {{{\cal R}^n}} \right),\,1 \leqslant p \leqslant \infty, 1 \leqslant \theta \leqslant \infty %$, be the anisotropic Besov classes of functions. The uniform bounds of truncation error is estimated for f ∈ Bυ($ ℝ^{n} $) and satisfying the following decay condition:%${\left| {f(x)} \right| \leqslant \frac{A}{{(1 + {{\left| x \right|}^\delta })}},} \;\; {x = ({x_1},...,{x_n}) \in {{\cal R}^n},}%$associated with the Shannon multidimensional sampling representation. The bounds of aliasing error for %$f\, \in \,B_{{\infty ^\theta }}^r\left( {{{\cal R}^n}} \right)%$ and satisfying the same decay condition as above is also evaluated. Truncation error (dpeaa)DE-He213 aliasing error (dpeaa)DE-He213 band-limited function (dpeaa)DE-He213 anisotropic Besov class of functions (dpeaa)DE-He213 Gensun, F. verfasserin aut Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 2(2003), 2 vom: 01. Mai, Seite 103-115 (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:2 year:2003 number:2 day:01 month:05 pages:103-115 https://dx.doi.org/10.1007/BF03549388 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2 2003 2 01 05 103-115 |
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10.1007/BF03549388 doi (DE-627)SPR043387233 (SPR)BF03549388-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 ASE Jingfan, L. verfasserin aut On Uniform Truncation Error Bounds and Aliasing Error for Multidimensional Sampling Expansion 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SIP 2003 Abstract Let Bυ($ ℝ_{n} $), %$\silon = ({\silon _1},...,{\silon _n}) \in {\cal R}_ + ^n%$, be the set of entire functions of exponential type υ bounded on $ ℝ^{n} $ and %$B_{{p^\theta }}^r\left( {{{\cal R}^n}} \right),\,1 \leqslant p \leqslant \infty, 1 \leqslant \theta \leqslant \infty %$, be the anisotropic Besov classes of functions. The uniform bounds of truncation error is estimated for f ∈ Bυ($ ℝ^{n} $) and satisfying the following decay condition:%${\left| {f(x)} \right| \leqslant \frac{A}{{(1 + {{\left| x \right|}^\delta })}},} \;\; {x = ({x_1},...,{x_n}) \in {{\cal R}^n},}%$associated with the Shannon multidimensional sampling representation. The bounds of aliasing error for %$f\, \in \,B_{{\infty ^\theta }}^r\left( {{{\cal R}^n}} \right)%$ and satisfying the same decay condition as above is also evaluated. Truncation error (dpeaa)DE-He213 aliasing error (dpeaa)DE-He213 band-limited function (dpeaa)DE-He213 anisotropic Besov class of functions (dpeaa)DE-He213 Gensun, F. verfasserin aut Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 2(2003), 2 vom: 01. Mai, Seite 103-115 (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:2 year:2003 number:2 day:01 month:05 pages:103-115 https://dx.doi.org/10.1007/BF03549388 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2 2003 2 01 05 103-115 |
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10.1007/BF03549388 doi (DE-627)SPR043387233 (SPR)BF03549388-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 ASE Jingfan, L. verfasserin aut On Uniform Truncation Error Bounds and Aliasing Error for Multidimensional Sampling Expansion 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SIP 2003 Abstract Let Bυ($ ℝ_{n} $), %$\silon = ({\silon _1},...,{\silon _n}) \in {\cal R}_ + ^n%$, be the set of entire functions of exponential type υ bounded on $ ℝ^{n} $ and %$B_{{p^\theta }}^r\left( {{{\cal R}^n}} \right),\,1 \leqslant p \leqslant \infty, 1 \leqslant \theta \leqslant \infty %$, be the anisotropic Besov classes of functions. The uniform bounds of truncation error is estimated for f ∈ Bυ($ ℝ^{n} $) and satisfying the following decay condition:%${\left| {f(x)} \right| \leqslant \frac{A}{{(1 + {{\left| x \right|}^\delta })}},} \;\; {x = ({x_1},...,{x_n}) \in {{\cal R}^n},}%$associated with the Shannon multidimensional sampling representation. The bounds of aliasing error for %$f\, \in \,B_{{\infty ^\theta }}^r\left( {{{\cal R}^n}} \right)%$ and satisfying the same decay condition as above is also evaluated. Truncation error (dpeaa)DE-He213 aliasing error (dpeaa)DE-He213 band-limited function (dpeaa)DE-He213 anisotropic Besov class of functions (dpeaa)DE-He213 Gensun, F. verfasserin aut Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 2(2003), 2 vom: 01. Mai, Seite 103-115 (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:2 year:2003 number:2 day:01 month:05 pages:103-115 https://dx.doi.org/10.1007/BF03549388 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2 2003 2 01 05 103-115 |
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10.1007/BF03549388 doi (DE-627)SPR043387233 (SPR)BF03549388-e DE-627 ger DE-627 rakwb eng 510 004 ASE 510 ASE Jingfan, L. verfasserin aut On Uniform Truncation Error Bounds and Aliasing Error for Multidimensional Sampling Expansion 2003 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SIP 2003 Abstract Let Bυ($ ℝ_{n} $), %$\silon = ({\silon _1},...,{\silon _n}) \in {\cal R}_ + ^n%$, be the set of entire functions of exponential type υ bounded on $ ℝ^{n} $ and %$B_{{p^\theta }}^r\left( {{{\cal R}^n}} \right),\,1 \leqslant p \leqslant \infty, 1 \leqslant \theta \leqslant \infty %$, be the anisotropic Besov classes of functions. The uniform bounds of truncation error is estimated for f ∈ Bυ($ ℝ^{n} $) and satisfying the following decay condition:%${\left| {f(x)} \right| \leqslant \frac{A}{{(1 + {{\left| x \right|}^\delta })}},} \;\; {x = ({x_1},...,{x_n}) \in {{\cal R}^n},}%$associated with the Shannon multidimensional sampling representation. The bounds of aliasing error for %$f\, \in \,B_{{\infty ^\theta }}^r\left( {{{\cal R}^n}} \right)%$ and satisfying the same decay condition as above is also evaluated. Truncation error (dpeaa)DE-He213 aliasing error (dpeaa)DE-He213 band-limited function (dpeaa)DE-He213 anisotropic Besov class of functions (dpeaa)DE-He213 Gensun, F. verfasserin aut Enthalten in Sampling theory, signal processing, and data analysis [Cham] : Birkhäuser, 2021 2(2003), 2 vom: 01. Mai, Seite 103-115 (DE-627)1735681601 (DE-600)3041928-1 2730-5724 nnns volume:2 year:2003 number:2 day:01 month:05 pages:103-115 https://dx.doi.org/10.1007/BF03549388 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2 2003 2 01 05 103-115 |
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on uniform truncation error bounds and aliasing error for multidimensional sampling expansion |
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On Uniform Truncation Error Bounds and Aliasing Error for Multidimensional Sampling Expansion |
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Abstract Let Bυ($ ℝ_{n} $), %$\silon = ({\silon _1},...,{\silon _n}) \in {\cal R}_ + ^n%$, be the set of entire functions of exponential type υ bounded on $ ℝ^{n} $ and %$B_{{p^\theta }}^r\left( {{{\cal R}^n}} \right),\,1 \leqslant p \leqslant \infty, 1 \leqslant \theta \leqslant \infty %$, be the anisotropic Besov classes of functions. The uniform bounds of truncation error is estimated for f ∈ Bυ($ ℝ^{n} $) and satisfying the following decay condition:%${\left| {f(x)} \right| \leqslant \frac{A}{{(1 + {{\left| x \right|}^\delta })}},} \;\; {x = ({x_1},...,{x_n}) \in {{\cal R}^n},}%$associated with the Shannon multidimensional sampling representation. The bounds of aliasing error for %$f\, \in \,B_{{\infty ^\theta }}^r\left( {{{\cal R}^n}} \right)%$ and satisfying the same decay condition as above is also evaluated. © SIP 2003 |
| abstractGer |
Abstract Let Bυ($ ℝ_{n} $), %$\silon = ({\silon _1},...,{\silon _n}) \in {\cal R}_ + ^n%$, be the set of entire functions of exponential type υ bounded on $ ℝ^{n} $ and %$B_{{p^\theta }}^r\left( {{{\cal R}^n}} \right),\,1 \leqslant p \leqslant \infty, 1 \leqslant \theta \leqslant \infty %$, be the anisotropic Besov classes of functions. The uniform bounds of truncation error is estimated for f ∈ Bυ($ ℝ^{n} $) and satisfying the following decay condition:%${\left| {f(x)} \right| \leqslant \frac{A}{{(1 + {{\left| x \right|}^\delta })}},} \;\; {x = ({x_1},...,{x_n}) \in {{\cal R}^n},}%$associated with the Shannon multidimensional sampling representation. The bounds of aliasing error for %$f\, \in \,B_{{\infty ^\theta }}^r\left( {{{\cal R}^n}} \right)%$ and satisfying the same decay condition as above is also evaluated. © SIP 2003 |
| abstract_unstemmed |
Abstract Let Bυ($ ℝ_{n} $), %$\silon = ({\silon _1},...,{\silon _n}) \in {\cal R}_ + ^n%$, be the set of entire functions of exponential type υ bounded on $ ℝ^{n} $ and %$B_{{p^\theta }}^r\left( {{{\cal R}^n}} \right),\,1 \leqslant p \leqslant \infty, 1 \leqslant \theta \leqslant \infty %$, be the anisotropic Besov classes of functions. The uniform bounds of truncation error is estimated for f ∈ Bυ($ ℝ^{n} $) and satisfying the following decay condition:%${\left| {f(x)} \right| \leqslant \frac{A}{{(1 + {{\left| x \right|}^\delta })}},} \;\; {x = ({x_1},...,{x_n}) \in {{\cal R}^n},}%$associated with the Shannon multidimensional sampling representation. The bounds of aliasing error for %$f\, \in \,B_{{\infty ^\theta }}^r\left( {{{\cal R}^n}} \right)%$ and satisfying the same decay condition as above is also evaluated. © SIP 2003 |
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| title_short |
On Uniform Truncation Error Bounds and Aliasing Error for Multidimensional Sampling Expansion |
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https://dx.doi.org/10.1007/BF03549388 |
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Gensun, F. |
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Gensun, F. |
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| doi_str |
10.1007/BF03549388 |
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2024-07-03T18:20:51.507Z |
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