Integral Geometry and Convolution Equations

V. V. Volchkov
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V. V. Volchkov: Donetsk National University, Department of Mathematics

in Springer Books from Springer

Date: 2003
ISBN: 978-94-010-0023-9
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Chapters in this book:

Ch Chapter 1 Sets with the Pompeiu Property

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Ch Chapter 1 Functions with Zero Averages Over Balls on Subsets of the Space ℝ n

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Ch Chapter 1 Injectivity Sets for Spherical Radon Transform

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Ch Chapter 1 One-Dimensional Case

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Ch Chapter 1 Sets and Mappings

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Ch Chapter 2 Some Questions of Approximation Theory

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Ch Chapter 2 General Solution of Convolution Equation in Domains with Spherical Symmetry

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Ch Chapter 2 Averages Over Balls on Hyperbolic Spaces

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Ch Chapter 2 Some Classes of Functions

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Ch Chapter 2 Functions with Vanishing Integrals Over Parallelepipeds

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Ch Chapter 3 Functions with Zero Integrals Over Spherical Caps

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Ch Chapter 3 Behavior of Solutions of Convolution Equation at Infinity

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Ch Chapter 3 Polyhedra with Local Pompeiu Property

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Ch Chapter 3 Gap Theorems

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Ch Chapter 3 Distributions

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Ch Chapter 4 Comments and Open Problems

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Ch Chapter 4 Some Special Functions

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Ch Chapter 4 Functions with Vanishing Integrals over Ellipsoids

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Ch Chapter 4 Morera Type Theorems

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Ch Chapter 4 Systems of Convolution Equations

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Ch Chapter 5 Other Sets with Local Pompeiu Property

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Ch Chapter 5 Comments and Open Problems

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Ch Chapter 5 Some Results Related to Spherical Harmonics

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Ch Chapter 5 Mean Value Characterization of Various Classes of Functions

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Ch Chapter 6 Applications to Partial Differential Equations

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Ch Chapter 6 Fourier Transform and Related Questions

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Ch Chapter 6 The ‘Three Squares’ Problem and Related Questions

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Ch Chapter 7 Some Questions of Measure Theory

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Ch Chapter 7 Injectivity Sets of the Pompeiu Transform

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Ch Chapter 7 Partial Differential Equations

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Ch Chapter 8 Radon Transform Over Hyperplanes

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Ch Chapter 8 Comments and Open Problems

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Ch Chapter 8 Functions with Zero Integrals in Problems of the Discrete Geometry

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Ch Chapter 9 Comments and Open Problems

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Ch Chapter 9 Comments and Open Problems

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DOI: 10.1007/978-94-010-0023-9

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