Fractional integrals and potentials
著者
書誌事項
Fractional integrals and potentials
（Pitman monographs and surveys in pure and applied mathematics, 82）
Longman, 1996
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注記
Bibliography: p. 397-409
内容説明・目次
内容説明
This volume presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. Beyond some basic properties of fractional integrals in one and many dimensions, it contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaudis approach and its generalization, leading to wavelet type representations.
目次
Preface
Notation
Chapter 1 Generalities
Chapter 2 One-dimensional fractional integrals
Chapter 3 Fractional integro-differentiation via wavelet transforms
Chapter 4 Riesz potentials on R
Chapter 5 Oscillatory potentials on R
Chapter 6 Potentials on a half-space
Chapter 7 Riesz potentials on a ball
Chapter 8 Fractional integrals on a sphere
Appendix 1
Appendix 2
Appendix 3
Bibliography
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