Applied Hyperfunction Theory - Couverture rigide

Imai, Isao

 
9780792315070: Applied Hyperfunction Theory
Couverture rigide
ISBN 10 : 0792315073 ISBN 13 : 9780792315070
Editeur : Kluwer Academic Publishers, 1992

Synopsis

Generalized functions are now widely recognized as important mathematical tools for engineers and physicists. But they are considered to be inaccessible for non-specialists. To remedy this situation, this book gives an intelligible exposition of generalized functions based on Sato's hyperfunction, which is essentially the `boundary value of analytic functions'. An intuitive image -- hyperfunction = vortex layer -- is adopted, and only an elementary knowledge of complex function theory is assumed. The treatment is entirely self-contained.
The first part of the book gives a detailed account of fundamental operations such as the four arithmetical operations applicable to hyperfunctions, namely differentiation, integration, and convolution, as well as Fourier transform. Fourier series are seen to be nothing but periodic hyperfunctions. In the second part, based on the general theory, the Hilbert transform and Poisson-Schwarz integral formula are treated and their application to integral equations is studied. A great number of formulas obtained in the course of treatment are summarized as tables in the appendix. In particular, those concerning convolution, the Hilbert transform and Fourier transform contain much new material.
For mathematicians, mathematical physicists and engineers whose work involves generalized functions.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Generalized functions are now widely recognized as important mathematical tools for engineers and physicists. But they are considered to be inaccessible for non-specialists. To remedy this situation, this book gives an intelligible exposition of generalized functions based on Sato's hyperfunction, which is essentially the `boundary value of analytic functions'. An intuitive image -- hyperfunction = vortex layer -- is adopted, and only an elementary knowledge of complex function theory is assumed. The treatment is entirely self-contained.
The first part of the book gives a detailed account of fundamental operations such as the four arithmetical operations applicable to hyperfunctions, namely differentiation, integration, and convolution, as well as Fourier transform. Fourier series are seen to be nothing but periodic hyperfunctions. In the second part, based on the general theory, the Hilbert transform and Poisson-Schwarz integral formula are treated and their application to integral equations is studied. A great number of formulas obtained in the course of treatment are summarized as tables in the appendix. In particular, those concerning convolution, the Hilbert transform and Fourier transform contain much new material.
For mathematicians, mathematical physicists and engineers whose work involves generalized functions.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Kluwer Academic Publishers
Date d'édition
1992
Langue
anglais
ISBN 10 
0792315073
ISBN 13 
9780792315070
Reliure
Relié
Nombre de pages
457
Coordonnées du fabricant
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Poststr. 9
Darmstadt
64293
Allemagne

Autres éditions populaires du même titre

9789401051255: Applied Hyperfunction Theory

Edition présentée

ISBN 10 :  9401051259 ISBN 13 :  9789401051255
Editeur : Springer, 2012
Couverture souple