Theory And Applications Of Convolution Integral Equations Book

	Preface
	Acknowledgements
	Introduction
Ch. 1	Preliminaries on Special Function Kernels
1.1	Algebraic kernels	1
1.2	Exponential, logarithmic, and trigonometric kernels	2
1.3	Chebyshev polynomials	3
1.4	Legendre polynomials and functions	4
1.5	Gegenbauer and Jacobi polynomials	5
1.6	Laguerre and Hermite polynomials	6
1.7	Bessel functions	7
1.8	Kummer's and Whittaker's functions	8
1.9	Gauss' hypergeometric function	9
1.10	Generalized hypergeometric and other functions	10
1.11	Further integral equations with multivariable kernels	13
Ch. 2	Basic Properties and Theorems
2.1	Convolutions and relations among equations	15
2.2	The Theorem of Titchmarsh and the uniqueness of solutions	19
2.3	Associated integral transformations	20
2.4	Associated fractional integrals	21
2.5	Simple kernel variations	24
Ch. 3	Methods and Illustrative Examples
3.1	Rodrigues' formula	26
3.2	Resolvent kernel	27
3.3	Laplace transformation	29
3.4	Mellin and other transformations	42
3.5	Fractional integrals	45
3.6	Mikusinski operators	48
3.7	Other methods	53
Ch. 4	Miscellaneous Results and Open Questions
4.1	Some immediate consequences from tables of integral transforms	56
4.2	Simplifications of generalized hypergeometric kernels	59
4.3	Confluent hypergeometric functions of several variables	64
4.4	Some open questions	68
Ch. 5	Equations of the Second and Other Kinds
5.1	General properties of equations of the second kind	70
5.2	Algebraic kernels	72
5.3	Exponential, trigonometric, and hyperbolic kernels	73
5.4	Higher transcendental functions	75
5.5	Integro-differential equations	76
5.6	Equations of the third kind	77
5.7	Non-linear equations	79
Ch. 6	Convolutions Over Other Intervals
6.1	Equations on the interval (x,[actual symbol not reproducible])	81
6.2	Equations on the interval (x,[actual symbol not reproducible])	84
6.3	Equations on the interval (0,[actual symbol not reproducible])	86
6.4	Equations on the interval ([actual symbol not reproducible])	100
6.5	Equations on the interval [a,b]	101
	Appendix. List of Symbols	104
	Inversion Tables. Index	114
	Bibliography	195
	Author Index	230
	Subject Index	234