Ramified Integrals, Singularities and Lacunas:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1995
|
| Schriftenreihe: | Mathematics and Its Applications
315 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Many special functions occuring in physics and partial differential equations can be represented by integral transformatIons: the fundamental solutions of many PDE's, Newton-Coulomb potentials, hypergeometric functions, Feynman integrals, initial data of (inverse) tomography problems, etc. The general picture of such transformations is as follows. There is an analytic fibre bundle E --+ T, a differential form w on E, whose restrictions on the fibres are closed, and a family of cycles in these fibres, parametrized by the points of T and depending continuously on these points. Then the integral of the form w along these cycles is a function on the base. The analytic properties of such functions depend on the monodromy action, i.e., on the natural action of the fundamental group of the base in the homology of the fibre: this action on the integration cycles defines the ramification of the analytic continuation of our function. The study of this action (which is a purely topological problem) can answer questions about the analytic behaviour of the integral function, for instance, is this function single-valued or at least algebraic, what are the singular points of this function, and what is its asymptotics close to these points. In this book, we study such analytic properties of three famous classes of functions: the volume functions, which appear in the Archimedes-Newton problem on integrable bodies; the Newton-Coulomb potentials, and the Green functions of hyperbolic equations (studied, in particular, in the Hadamard-Petrovskii-Atiyah-Bott-Garding lacuna theory) |
| Beschreibung: | 1 Online-Ressource (XVII, 294 p) |
| ISBN: | 9789401102131 9789401040952 |
| DOI: | 10.1007/978-94-011-0213-1 |
Internformat
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| 245 | 1 | 0 | |a Ramified Integrals, Singularities and Lacunas |c by V. A. Vassiliev |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 1995 | |
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| 490 | 1 | |a Mathematics and Its Applications |v 315 | |
| 500 | |a Many special functions occuring in physics and partial differential equations can be represented by integral transformatIons: the fundamental solutions of many PDE's, Newton-Coulomb potentials, hypergeometric functions, Feynman integrals, initial data of (inverse) tomography problems, etc. The general picture of such transformations is as follows. There is an analytic fibre bundle E --+ T, a differential form w on E, whose restrictions on the fibres are closed, and a family of cycles in these fibres, parametrized by the points of T and depending continuously on these points. Then the integral of the form w along these cycles is a function on the base. The analytic properties of such functions depend on the monodromy action, i.e., on the natural action of the fundamental group of the base in the homology of the fibre: this action on the integration cycles defines the ramification of the analytic continuation of our function. The study of this action (which is a purely topological problem) can answer questions about the analytic behaviour of the integral function, for instance, is this function single-valued or at least algebraic, what are the singular points of this function, and what is its asymptotics close to these points. In this book, we study such analytic properties of three famous classes of functions: the volume functions, which appear in the Archimedes-Newton problem on integrable bodies; the Newton-Coulomb potentials, and the Green functions of hyperbolic equations (studied, in particular, in the Hadamard-Petrovskii-Atiyah-Bott-Garding lacuna theory) | ||
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-search | 515.72 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-011-0213-1 |
| format | Electronic eBook |
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| id | DE-604.BV042423813 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401102131 9789401040952 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859230 |
| oclc_num | 863677156 |
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| physical | 1 Online-Ressource (XVII, 294 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer Netherlands |
| record_format | marc |
| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spelling | Vassiliev, V. A. Verfasser aut Ramified Integrals, Singularities and Lacunas by V. A. Vassiliev Dordrecht Springer Netherlands 1995 1 Online-Ressource (XVII, 294 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 315 Many special functions occuring in physics and partial differential equations can be represented by integral transformatIons: the fundamental solutions of many PDE's, Newton-Coulomb potentials, hypergeometric functions, Feynman integrals, initial data of (inverse) tomography problems, etc. The general picture of such transformations is as follows. There is an analytic fibre bundle E --+ T, a differential form w on E, whose restrictions on the fibres are closed, and a family of cycles in these fibres, parametrized by the points of T and depending continuously on these points. Then the integral of the form w along these cycles is a function on the base. The analytic properties of such functions depend on the monodromy action, i.e., on the natural action of the fundamental group of the base in the homology of the fibre: this action on the integration cycles defines the ramification of the analytic continuation of our function. The study of this action (which is a purely topological problem) can answer questions about the analytic behaviour of the integral function, for instance, is this function single-valued or at least algebraic, what are the singular points of this function, and what is its asymptotics close to these points. In this book, we study such analytic properties of three famous classes of functions: the volume functions, which appear in the Archimedes-Newton problem on integrable bodies; the Newton-Coulomb potentials, and the Green functions of hyperbolic equations (studied, in particular, in the Hadamard-Petrovskii-Atiyah-Bott-Garding lacuna theory) Mathematics Geometry, algebraic Integral Transforms Differential equations, partial Potential theory (Mathematics) Cell aggregation / Mathematics Integral Transforms, Operational Calculus Algebraic Geometry Partial Differential Equations Manifolds and Cell Complexes (incl. Diff.Topology) Potential Theory Mathematik Mathematics and Its Applications 315 (DE-604)BV008163334 315 https://doi.org/10.1007/978-94-011-0213-1 Verlag Volltext |
| spellingShingle | Vassiliev, V. A. Ramified Integrals, Singularities and Lacunas Mathematics and Its Applications Mathematics Geometry, algebraic Integral Transforms Differential equations, partial Potential theory (Mathematics) Cell aggregation / Mathematics Integral Transforms, Operational Calculus Algebraic Geometry Partial Differential Equations Manifolds and Cell Complexes (incl. Diff.Topology) Potential Theory Mathematik |
| title | Ramified Integrals, Singularities and Lacunas |
| title_auth | Ramified Integrals, Singularities and Lacunas |
| title_exact_search | Ramified Integrals, Singularities and Lacunas |
| title_full | Ramified Integrals, Singularities and Lacunas by V. A. Vassiliev |
| title_fullStr | Ramified Integrals, Singularities and Lacunas by V. A. Vassiliev |
| title_full_unstemmed | Ramified Integrals, Singularities and Lacunas by V. A. Vassiliev |
| title_short | Ramified Integrals, Singularities and Lacunas |
| title_sort | ramified integrals singularities and lacunas |
| topic | Mathematics Geometry, algebraic Integral Transforms Differential equations, partial Potential theory (Mathematics) Cell aggregation / Mathematics Integral Transforms, Operational Calculus Algebraic Geometry Partial Differential Equations Manifolds and Cell Complexes (incl. Diff.Topology) Potential Theory Mathematik |
| topic_facet | Mathematics Geometry, algebraic Integral Transforms Differential equations, partial Potential theory (Mathematics) Cell aggregation / Mathematics Integral Transforms, Operational Calculus Algebraic Geometry Partial Differential Equations Manifolds and Cell Complexes (incl. Diff.Topology) Potential Theory Mathematik |
| url | https://doi.org/10.1007/978-94-011-0213-1 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT vassilievva ramifiedintegralssingularitiesandlacunas |