Introduction to the Theory of Singular Integral Operators with Shift

Abstract

Introductlon to the theory of singular lntegral operators .,th shlft I by V,ctor G. Kravchenko and G.orgll S. Lltvlnchuk. p. cm. --(Mathematlcs and ltS appl icatlons ; v. 289) Includes blbllographlcal references and index.

Метод Оценки Собственных Функций Некоторых Классов Интегральных Операторов В Неограниченных Областях

“…Результаты, аналогичные сформулированным выше, справедливы для многомерных операторов свертки в конусах, условия нётеровости которых получены в [15], и для одномерных операторов Винера-Хопфа с осциллирую-щими коэффициентами, для которых условия нётеровости могут быть получе-ны из соответствующей теории для сингулярных интегральных операторов с некарлемановским сдвигом (см. [16], [17]). …”

On the Application of New Convergence Criteria for Kantorovich Method to Nonlinear Singular Integral Equation with Shift

“…There is a literature on the successful development of the nonlinear singular integral equations with shift (NSIES) [1,3,4,15,18,20]. The Noether theory of singular integral operators with shift (SIOS) is developed for a closed and open contour ( [2,10,13,14,16,18] and others). The theory of singular integral equations with shift (SIES) is an important part of integral equations because of its recent applications in many fields of physics and engineering, [6,14,16].…”

One-sided invertibility of binomial functional operators with a shift on rearrangement-invariant spaces

“…It is known that if α preserves the orientation on Γ then all periodic points of α have the same multiplicity [16, Theorem 1.3.1]. If α changes the orientation on Γ then α has two fixed points on Γ, and all other periodic points of α (if they exist) have the multiplicity two [16,Theorem 1.3.2]. Clearly, the set Λ is closed.…”