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Hyper-Holomorphic Cells and Fredholm Theory
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G. Khimshiashvili
Published/Copyright:
February 24, 2010
Abstract
We deal with differentiable cells defined by solutions to certain linear elliptic systems of first order. It turns out that in some cases families of such cells attached to a given submanifold may be described by Fredholm operators in appropriate function spaces. Using the previous results of the author on the existence of elliptic Riemann–Hilbert problems for generalized Cauchy–Riemann systems, we indicate some classes of systems which give rise to non-linear Fredholm operators of such type.
Key words and phrases:: Generalized Cauchy–Riemann system; Clifford algebra; elliptic cell; hyper-holomorphic mapping; Riemann–Hilbert problem; Fredholm operator
Received: 2001-05-01
Published Online: 2010-02-24
Published in Print: 2001-September
© Heldermann Verlag
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Keywords for this article
Generalized Cauchy–Riemann system;
Clifford algebra;
elliptic cell;
hyper-holomorphic mapping;
Riemann–Hilbert problem;
Fredholm operator
Articles in the same Issue
- A New Method of Solving the Basic Plane Boundary Value Problems of Statics of the Elastic Mixture Theory
- Euler Polynomials and the Related Quadrature Rule
- MD-Numbers and Asymptotic MD-Numbers of Operators
- Boundary Variational Inequality Approach in the Anisotropic Elasticity for the Signorini Problem
- On Vector Sums of Measure Zero Sets
- Hyper-Holomorphic Cells and Fredholm Theory
- On a Representation of the Derivative of a Conformal Mapping
- On a Trace Inequality for One-Sided Potentials and Applications to the Solvability of Nonlinear Integral Equations
- Quasiconformal Deformations of Holomorphic Functions
- Convolutional Codes and Frequency Responses
- Boundary Integral Equations of Plane Elasticity in Domains with Peaks
- Pluriregular, Plurigeneralized Regular Equations in Clifford Analysis
- On Volterra Type Singular Integral Equations
