Description
Introduction to the Theory of Singular Integral Operators with Shift, 1994
Mathematics and Its Applications Series, Vol. 289
Authors: Kravchenko Viktor G., Litvinchuk Georgii S.
Language: EnglishKeywords
DEX; Finite; Integral equation; Singular integral; algebra; dynamical systems; equation; form; function; functional; information; integral; kernel; operator; proof
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Publication date: 12-2012
288 p. · 16x24 cm · Paperback
288 p. · 16x24 cm · Paperback
Description
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Background information. Noetherity criterion and a formula for the index of a singular integral functional operator of first order in the continuous case. The Noether theory of a singular integral functional operator of finite order in the continuous case. The Noether theory of singular integral functional operators with continuous coefficients on a non-closed contour. The Noether theory in algebras of singular integral functional operators.
1. Background information.- 2.Noetherity criterion and a formula for the index of a singular integral functional operator of first order in the continuous case.- 3. The Noether theory of a singular integral functional operator of finite order in the continuous case.- 4. The Noether theory of singular integral functional operators with continuous coefficients on a non-closed contour.- 5. The Noether theory in algebras of singular integral functional operators.- References.
This book is devoted to the Fredholm theory of singular integral operators with shift Lp, 1_ spaces. Fredholm criteria are derived and the indices of the Fredholm operators are computed. Simultaneously, a theory of continuous invertibility for functional operators is constructed, and its relation to the theory of dynamical systems is discussed. Also, a new systematic approach to the Fredholm theory of classical singular integral equations with Cauchy kernel is proposed.
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