Discrete Simulation of a Class of Distributed Systems Using Functional Analytic Methods
Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For t...
Ausführliche Beschreibung
Autor*in: |
Dymkou, Vitali [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
2006 |
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Schlagwörter: |
Partial differential equations |
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Anmerkung: |
© Springer Science+Business Media, LLC 2006 |
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Übergeordnetes Werk: |
Enthalten in: Multidimensional systems and signal processing - Kluwer Academic Publishers, 1990, 17(2006), 2-3 vom: Juli, Seite 177-209 |
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Übergeordnetes Werk: |
volume:17 ; year:2006 ; number:2-3 ; month:07 ; pages:177-209 |
Links: |
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DOI / URN: |
10.1007/s11045-005-6234-5 |
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Katalog-ID: |
OLC2048104509 |
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520 | |a Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing. | ||
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10.1007/s11045-005-6234-5 doi (DE-627)OLC2048104509 (DE-He213)s11045-005-6234-5-p DE-627 ger DE-627 rakwb eng 510 VZ Dymkou, Vitali verfasserin aut Discrete Simulation of a Class of Distributed Systems Using Functional Analytic Methods 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2006 Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing. Multi-dimensional systems Partial differential equations Frequency domain Multi-functional transformations Spectral theory Rabenstein, Rudolf aut Steffen, Peter aut Enthalten in Multidimensional systems and signal processing Kluwer Academic Publishers, 1990 17(2006), 2-3 vom: Juli, Seite 177-209 (DE-627)130892076 (DE-600)1041098-3 (DE-576)038686074 0923-6082 nnns volume:17 year:2006 number:2-3 month:07 pages:177-209 https://doi.org/10.1007/s11045-005-6234-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 17 2006 2-3 07 177-209 |
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10.1007/s11045-005-6234-5 doi (DE-627)OLC2048104509 (DE-He213)s11045-005-6234-5-p DE-627 ger DE-627 rakwb eng 510 VZ Dymkou, Vitali verfasserin aut Discrete Simulation of a Class of Distributed Systems Using Functional Analytic Methods 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2006 Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing. Multi-dimensional systems Partial differential equations Frequency domain Multi-functional transformations Spectral theory Rabenstein, Rudolf aut Steffen, Peter aut Enthalten in Multidimensional systems and signal processing Kluwer Academic Publishers, 1990 17(2006), 2-3 vom: Juli, Seite 177-209 (DE-627)130892076 (DE-600)1041098-3 (DE-576)038686074 0923-6082 nnns volume:17 year:2006 number:2-3 month:07 pages:177-209 https://doi.org/10.1007/s11045-005-6234-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 17 2006 2-3 07 177-209 |
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10.1007/s11045-005-6234-5 doi (DE-627)OLC2048104509 (DE-He213)s11045-005-6234-5-p DE-627 ger DE-627 rakwb eng 510 VZ Dymkou, Vitali verfasserin aut Discrete Simulation of a Class of Distributed Systems Using Functional Analytic Methods 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2006 Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing. Multi-dimensional systems Partial differential equations Frequency domain Multi-functional transformations Spectral theory Rabenstein, Rudolf aut Steffen, Peter aut Enthalten in Multidimensional systems and signal processing Kluwer Academic Publishers, 1990 17(2006), 2-3 vom: Juli, Seite 177-209 (DE-627)130892076 (DE-600)1041098-3 (DE-576)038686074 0923-6082 nnns volume:17 year:2006 number:2-3 month:07 pages:177-209 https://doi.org/10.1007/s11045-005-6234-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 17 2006 2-3 07 177-209 |
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10.1007/s11045-005-6234-5 doi (DE-627)OLC2048104509 (DE-He213)s11045-005-6234-5-p DE-627 ger DE-627 rakwb eng 510 VZ Dymkou, Vitali verfasserin aut Discrete Simulation of a Class of Distributed Systems Using Functional Analytic Methods 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2006 Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing. Multi-dimensional systems Partial differential equations Frequency domain Multi-functional transformations Spectral theory Rabenstein, Rudolf aut Steffen, Peter aut Enthalten in Multidimensional systems and signal processing Kluwer Academic Publishers, 1990 17(2006), 2-3 vom: Juli, Seite 177-209 (DE-627)130892076 (DE-600)1041098-3 (DE-576)038686074 0923-6082 nnns volume:17 year:2006 number:2-3 month:07 pages:177-209 https://doi.org/10.1007/s11045-005-6234-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 17 2006 2-3 07 177-209 |
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10.1007/s11045-005-6234-5 doi (DE-627)OLC2048104509 (DE-He213)s11045-005-6234-5-p DE-627 ger DE-627 rakwb eng 510 VZ Dymkou, Vitali verfasserin aut Discrete Simulation of a Class of Distributed Systems Using Functional Analytic Methods 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2006 Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing. Multi-dimensional systems Partial differential equations Frequency domain Multi-functional transformations Spectral theory Rabenstein, Rudolf aut Steffen, Peter aut Enthalten in Multidimensional systems and signal processing Kluwer Academic Publishers, 1990 17(2006), 2-3 vom: Juli, Seite 177-209 (DE-627)130892076 (DE-600)1041098-3 (DE-576)038686074 0923-6082 nnns volume:17 year:2006 number:2-3 month:07 pages:177-209 https://doi.org/10.1007/s11045-005-6234-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 17 2006 2-3 07 177-209 |
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Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing. © Springer Science+Business Media, LLC 2006 |
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Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing. © Springer Science+Business Media, LLC 2006 |
abstract_unstemmed |
Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing. © Springer Science+Business Media, LLC 2006 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2048104509</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503194522.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2006 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11045-005-6234-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2048104509</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11045-005-6234-5-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dymkou, Vitali</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Discrete Simulation of a Class of Distributed Systems Using Functional Analytic Methods</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2006</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, LLC 2006</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Multi-dimensional systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Partial differential equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Frequency domain</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Multi-functional transformations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Spectral theory</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rabenstein, Rudolf</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Steffen, Peter</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Multidimensional systems and signal processing</subfield><subfield code="d">Kluwer Academic Publishers, 1990</subfield><subfield code="g">17(2006), 2-3 vom: Juli, Seite 177-209</subfield><subfield code="w">(DE-627)130892076</subfield><subfield code="w">(DE-600)1041098-3</subfield><subfield code="w">(DE-576)038686074</subfield><subfield code="x">0923-6082</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:17</subfield><subfield code="g">year:2006</subfield><subfield code="g">number:2-3</subfield><subfield code="g">month:07</subfield><subfield code="g">pages:177-209</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s11045-005-6234-5</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">17</subfield><subfield code="j">2006</subfield><subfield code="e">2-3</subfield><subfield code="c">07</subfield><subfield code="h">177-209</subfield></datafield></record></collection>
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