Banach Algebras with Symbol and Singular Integral Operators:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser Basel
1987
|
| Series: | Operator Theory: Advances and Applications
26 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | About fifty years aga S. G. Mikhlin, in solving the regularization problem for two-dimensional singular integral operators [56], assigned to each such operator a function which he called a symbol, and showed that regularization is possible if the infimum of the modulus of the symbol is positive. Later, the notion of a symbol was extended to multidimensional singular integral operators (of arbitrary dimension) [57, 58, 21, 22]. Subsequently, the synthesis of singular integral, and differential operators [2, 8, 9]led to the theory of pseudodifferential operators [17, 35] (see also [35(1)-35(17)]*), which are naturally characterized by their symbols. An important role in the construction of symbols for many classes of operators was played by Gelfand's theory of maximal ideals of Banach algebras [201. Using this theory, criteria were obtained for Fredholmness of one-dimensional singular integral operators with continuous coefficients [34 (42)], Wiener-Hopf operators [37], and multidimensional singular integral operators [38 (2)]. The investigation of systems of equations involving such operators has led to the notion of matrix symbol [59, 12 (14), 39, 41]. This notion plays an essential role not only for systems, but also for singular integral operators with piecewise-continuous (scalar) coefficients [44 (4)]. At the same time, attempts to introduce a (scalar or matrix) symbol for other algebras have failed |
| Physical Description: | 1 Online-Ressource (X, 206 p) |
| ISBN: | 9783034854634 9783034854658 |
| DOI: | 10.1007/978-3-0348-5463-4 |
Staff View
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| 490 | 1 | |a Operator Theory: Advances and Applications |v 26 | |
| 500 | |a About fifty years aga S. G. Mikhlin, in solving the regularization problem for two-dimensional singular integral operators [56], assigned to each such operator a function which he called a symbol, and showed that regularization is possible if the infimum of the modulus of the symbol is positive. Later, the notion of a symbol was extended to multidimensional singular integral operators (of arbitrary dimension) [57, 58, 21, 22]. Subsequently, the synthesis of singular integral, and differential operators [2, 8, 9]led to the theory of pseudodifferential operators [17, 35] (see also [35(1)-35(17)]*), which are naturally characterized by their symbols. An important role in the construction of symbols for many classes of operators was played by Gelfand's theory of maximal ideals of Banach algebras [201. Using this theory, criteria were obtained for Fredholmness of one-dimensional singular integral operators with continuous coefficients [34 (42)], Wiener-Hopf operators [37], and multidimensional singular integral operators [38 (2)]. The investigation of systems of equations involving such operators has led to the notion of matrix symbol [59, 12 (14), 39, 41]. This notion plays an essential role not only for systems, but also for singular integral operators with piecewise-continuous (scalar) coefficients [44 (4)]. At the same time, attempts to introduce a (scalar or matrix) symbol for other algebras have failed | ||
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Record in the Search Index
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| id | DE-604.BV042421865 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9783034854634 9783034854658 |
| language | English |
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| publishDate | 1987 |
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| spelling | Krupnik, Nahum 1932- Verfasser (DE-588)121758400 aut Banach Algebras with Symbol and Singular Integral Operators by Naum Yakovlevich Krupnik Basel Birkhäuser Basel 1987 1 Online-Ressource (X, 206 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory: Advances and Applications 26 About fifty years aga S. G. Mikhlin, in solving the regularization problem for two-dimensional singular integral operators [56], assigned to each such operator a function which he called a symbol, and showed that regularization is possible if the infimum of the modulus of the symbol is positive. Later, the notion of a symbol was extended to multidimensional singular integral operators (of arbitrary dimension) [57, 58, 21, 22]. Subsequently, the synthesis of singular integral, and differential operators [2, 8, 9]led to the theory of pseudodifferential operators [17, 35] (see also [35(1)-35(17)]*), which are naturally characterized by their symbols. An important role in the construction of symbols for many classes of operators was played by Gelfand's theory of maximal ideals of Banach algebras [201. Using this theory, criteria were obtained for Fredholmness of one-dimensional singular integral operators with continuous coefficients [34 (42)], Wiener-Hopf operators [37], and multidimensional singular integral operators [38 (2)]. The investigation of systems of equations involving such operators has led to the notion of matrix symbol [59, 12 (14), 39, 41]. This notion plays an essential role not only for systems, but also for singular integral operators with piecewise-continuous (scalar) coefficients [44 (4)]. At the same time, attempts to introduce a (scalar or matrix) symbol for other algebras have failed Science (General) Science, general Naturwissenschaft Singulärer Integraloperator (DE-588)4131249-1 gnd rswk-swf Integraloperator (DE-588)4131247-8 gnd rswk-swf Fredholm-Theorie (DE-588)4155263-5 gnd rswk-swf Banach-Algebra (DE-588)4193187-7 gnd rswk-swf Banach-Algebra (DE-588)4193187-7 s Singulärer Integraloperator (DE-588)4131249-1 s 1\p DE-604 Fredholm-Theorie (DE-588)4155263-5 s 2\p DE-604 Integraloperator (DE-588)4131247-8 s 3\p DE-604 Operator Theory Advances and Applications 26 (DE-604)BV035421307 26 https://doi.org/10.1007/978-3-0348-5463-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Krupnik, Nahum 1932- Banach Algebras with Symbol and Singular Integral Operators Science (General) Science, general Naturwissenschaft Singulärer Integraloperator (DE-588)4131249-1 gnd Integraloperator (DE-588)4131247-8 gnd Fredholm-Theorie (DE-588)4155263-5 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| subject_GND | (DE-588)4131249-1 (DE-588)4131247-8 (DE-588)4155263-5 (DE-588)4193187-7 |
| title | Banach Algebras with Symbol and Singular Integral Operators |
| title_auth | Banach Algebras with Symbol and Singular Integral Operators |
| title_exact_search | Banach Algebras with Symbol and Singular Integral Operators |
| title_full | Banach Algebras with Symbol and Singular Integral Operators by Naum Yakovlevich Krupnik |
| title_fullStr | Banach Algebras with Symbol and Singular Integral Operators by Naum Yakovlevich Krupnik |
| title_full_unstemmed | Banach Algebras with Symbol and Singular Integral Operators by Naum Yakovlevich Krupnik |
| title_short | Banach Algebras with Symbol and Singular Integral Operators |
| title_sort | banach algebras with symbol and singular integral operators |
| topic | Science (General) Science, general Naturwissenschaft Singulärer Integraloperator (DE-588)4131249-1 gnd Integraloperator (DE-588)4131247-8 gnd Fredholm-Theorie (DE-588)4155263-5 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| topic_facet | Science (General) Science, general Naturwissenschaft Singulärer Integraloperator Integraloperator Fredholm-Theorie Banach-Algebra |
| url | https://doi.org/10.1007/978-3-0348-5463-4 |
| volume_link | (DE-604)BV035421307 |
| work_keys_str_mv | AT krupniknahum banachalgebraswithsymbolandsingularintegraloperators |