Generalized Analytic Functions in Fractional Spaces

Front Cover
CRC Press, May 19, 1997 - Mathematics - 160 pages
This book studies the foundations of the general theory of generalized analytic functions in fractional spaces. The employment of fractional spaces and embedding theorems support applications of the theory of generalized analytic functions. The results obtained are applicable to the theory of singular integral equations, boundary value problems for elliptic differential equations, functions of a complex variable, as well as the theory of plates and shells. The book will be of interest to scientific workers and specialists interested in these questions and likewise to advanced students in mechanical engineering faculties.
 

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Contents

Introduction
1
Properties of several integral operators in fractional spaces
6
Properties of the operators TGf and Ilgf in the spaces B G
14
Continuity of functions of the form Taf
23
Some properties of functions from BataG
30
Properties of the operators Tef and lief
33
On products of functions from Bclasses
37
Complete continuity of certain operators linked to Tof
41
Treatment of the nonlinear integral equation 4 3
70
Adjoint equation
72
Systems of basic elementary generalized analytic functions and basic kernels of the class VAB1 p 2 a 2p 1
73
Cauchys generalized formula
75
Expression for the resolvent operator in terms of the basic kernels
78
Representation of generalized analytic functions with the aid of generalized Cauchy type integrals
81
On continuously differentiable homeomorphic solutions
87
Boundary value problems
95

Properties of Cauchytype integrals
45
General theory of generalized analytic functions in fractional spaces
51
An integral equation
54
Differential properties of regular solutions
57
Further extensions of the solution concept A basic lemma and properties of generalized solutions
59
Solvability of integral equations of the form 2 1
64
Generalized analytic functions in unbounded domains
107
The properties of the operator Tf in Lpp 1
117
References
132
Index of Names
139
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