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1987
In this chapter a connection is established between the Fredholmness of the operator A = [A mk ] m,k=1 n in the Cartesian product E n = E × ... × E of n copies of a Banach space E and the Fredholmness of its determinant det[A mk ] in E. Conditions are given under which the indices of these two operators coincide.
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In this chapter a connection is established between the Fredholmness of the operator A = [A mk ] m,k=1 n in the Cartesian product E n = E × ... × E of n copies of a Banach space E and the Fredholmness of its determinant det[A mk ] in E. Conditions are given under which the indices of these two operators coincide.
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2011
The theory of linear Fredholm operators will be used in this chapter to study onlinear elliptic problems. Nonlinear operators are called Fredholm operators if the corresponding linearized operators satisfy this property.
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The theory of linear Fredholm operators will be used in this chapter to study onlinear elliptic problems. Nonlinear operators are called Fredholm operators if the corresponding linearized operators satisfy this property.
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2011
The theory of elliptic problems is essentially based on their Fredholm property which determines solvability conditions and a well-defined index. The Fredholm property and index are preserved under small perturbations of the operators. The situation is quite different if the Fredholm property is not satisfied. A general theory of such problems does not
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The theory of elliptic problems is essentially based on their Fredholm property which determines solvability conditions and a well-defined index. The Fredholm property and index are preserved under small perturbations of the operators. The situation is quite different if the Fredholm property is not satisfied. A general theory of such problems does not
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Fredholm weighted composition operators
Integral Equations and Operator Theory, 1993For a compact Hausdorff space \(X\) and some functional space \(F(X)\) on \(X\) a weighted composition operator is defined as \(uC_ \varphi f(x):=u(x)f(\varphi (x))\), where \(\varphi: X\to X\) is an automorphism. The author obtains criteria for the operator \(uC_ \varphi: C(X)\to C(X)\) to be a Fredholm operator and finds that in the case when \(X ...
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Compact and Fredholm Operators
1993The operators in infinite dimensional spaces closest to operators in finite dimensional spaces are the compact operators, which will now be studied systematically. A large number of examples of compact operators are given in the exercises.
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Holomorphic Fredholm Operator Functions
1993The purpose of this chapter is to set down some facts from operator theory, functional analysis and complex analysis that will be frequently used in the main body of the book. We do not intend to present here the whole theory of Fredholm operator functions, because it would take a book itself.
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