Sinossi
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.
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Contenuti
Series Editor's Preface. Preface. 1. Introduction. 2. Operations on Hyperfunctions. 3. Basic Hyperfunctions. 4. Hyperfunctions Depending on Parameters. 5. Fourier Transformation. 6. Fourier Transformation of Power-Type Hyperfunctions. 7. Upper (Lower)-Type Hyperfunctions. 8. Fourier Transforms - Existence and Regularity. 9. Fourier Transformation - Asymptotic Behaviour. 10. Periodic Hyperfunctions and Fourier Series. 11. Analytic Continuation and Projection of Hyperfunctions. 12. Products of Hyperfunctions. 13. Convolution of Hyperfunctions. 14. Convolution of Periodic Hyperfunctions. 15. Hilbert Transformation, Conjugate Hyperfunction. 16. Poisson-Schwarz Integration Formulae. 17. Integral Equations. 18. Laplace Transformation. Epilogue. References. Appendices A: Symbols. B: Functions, Hyperfunctions and Generating Functions. C: Special Functions. D: Power-Type Hyperfunctions with Negative Integer Power. E: Upper-Type and Lower-Type Hyperfunctions. F: Hyperfunctions and Generating Functions. G: Convolutions. H: Hilbert Transforms. I: Fourier Transforms. J: Laplace Transforms. K: Cosine Transforms and Sine Transforms. Index.
Product Description
Book by Imai Isao
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Applied Hyperfunction Theory
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Springer Netherlands Mai 1992, 1992
ISBN 10: 0792315073
ISBN 13: 9780792315070
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 464 pp. Englisch. Codice articolo 9780792315070
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 generali. Codice articolo 5966416
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Buch. Condizione: Neu. Applied Hyperfunction Theory | Isao Imai | Buch | Englisch | 1992 | Springer | EAN 9780792315070 | Verantwortliche Person für die EU: Springer Nature Customer Service Center GmbH, Europaplatz 3, 69115 Heidelberg, productsafety[at]springernature[dot]com | Anbieter: preigu Print on Demand. Codice articolo 102701374
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Applied Hyperfunction Theory
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 464 pp. Englisch. Codice articolo 9780792315070
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Applied Hyperfunction Theory
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ISBN 10: 0792315073
ISBN 13: 9780792315070
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9780792315070
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