Ramified Integrals, Singularities and Lacunas /
This volume contains an introduction to the Picard--Lefschetz theory, which controls the ramification and qualitative behaviour of many important functions of PDEs and integral geometry, and its foundations in singularity theory. <br/> Solutions to many problems of these theories are treated....
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht :
Springer Netherlands : Imprint : Springer,
1995.
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| Series: | Mathematics and its applications ;
315. |
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | This volume contains an introduction to the Picard--Lefschetz theory, which controls the ramification and qualitative behaviour of many important functions of PDEs and integral geometry, and its foundations in singularity theory. <br/> Solutions to many problems of these theories are treated. Subjects include the proof of multidimensional analogues of Newton's theorem on the nonintegrability of ovals; extension of the proofs for the theorems of Newton, Ivory, Arnold and Givental on potentials of algebraic surfaces. Also, it is discovered for which <em>d</em> and <em>n</em> the potentials of degree <em>d</em> hyperbolic surfaces in R<sup>n</sup> are algebraic outside the surfaces; the equivalence of local regularity (the so-called sharpness), of fundamental solutions of hyperbolic PDEs and the topological Petrovskii--Atiyah--Bott--Gårding condition is proved, and the geometrical characterization of domains of sharpness close to simple singularities of wave fronts is considered; a 'stratified' version of the Picard--Lefschetz formula is proved, and an algorithm enumerating topologically distinct Morsifications of real function singularities is given. <br/> This book will be valuable to those who are interested in integral transforms, operational calculus, algebraic geometry, PDEs, manifolds and cell complexes and potential theory. <br/> |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (304 pages) |
| ISBN: | 9789401102131 (electronic bk.) 9401102139 (electronic bk.) |