{"product_id":"one-dimensional-linear-singular-integral-equations-israel-gohberg-9783764327965","title":"One-Dimensional Linear Singular Integral Equations: Vol.II: General Theory and Applications","description":"6 Preliminaries.- 6.1 The operator of singular integration.- 6.2 The space Lp(?, ?).- 6.3 Singular integral operators.- 6.4 The spaces $$L_{p} { + }(\\Gamma, \\rho ), L_{p} { - }(\\Gamma, \\rho ) and \\mathop{{L_{p} { - }}}\\limits { \\circ } (\\Gamma, \\rho )$$.- 6.5 Factorization.- 6.6 One-sided invertibility of singular integral operators.- 6.7 Fredholm operators.- 6.8 The local principle for singular integral operators.- 6.9 The interpolation theorem.- 7 General theorems.- 7.1 Change of the curve.- 7.2 The quotient norm of singular integral operators.- 7.3 The principle of separation of singularities.- 7.4 A necessary condition.- 7.5 Theorems on kernel and cokernel of singular integral operators.- 7.6 Two theorems on connections between singular integral operators.- 7.7 Index cancellation and approximative inversion of singular integral operators.- 7.8 Exercises.- Comments and references.- 8 The generalized factorization of bounded measurable functions and its applications.- 8.1 Sketch of the problem.- 8.2 Functions admitting a generalized factorization with respect to a curve in Lp(?, ?).- 8.3 Factorization in the spaces Lp(?, ?).- 8.4 Application of the factorization to the inversion of singular integral operators.- 8.5 Exercises.- Comments and references.- 9 Singular integral operators with piecewise continuous coefficients and their applications.- 9.1 Non-singular functions and their index.- 9.2 Criteria for the generalized factorizability of power functions.- 9.3 The inversion of singular integral operators on a closed curve.- 9.4 Composed curves.- 9.5 Singular integral operators with continuous coefficients on a composed curve.- 9.6 The case of the real axis.- 9.7 Another method of inversion.- 9.8 Singular integral operators with regel functions coefficients.- 9.9 Estimates for the norms of the operators P?, Q? and S?.- 9.10 Singular operators on spaces H?o(?, ?).- 9.11 Singular operators on symmetric spaces.- 9.12 Fredholm conditions in the case of arbitrary weights.- 9.13 Technical lemmas.- 9.14 Toeplitz and paired operators with piecewise continuous coefficients on the spaces lp and ?p.- 9.15 Some applications.- 9.16 Exercises.- Comments and references.- 10 Singular integral operators on non-simple curves.- 10.1 Technical lemmas.- 10.2 A preliminary theorem.- 10.3 The main theorem.- 10.4 Exercises.- Comments and references.- 11 Singular integral operators with coefficients having discontinuities of almost periodic type.- 11.1 Almost periodic functions and their factorization.- 11.2 Lemmas on functions with discontinuities of almost periodic type.- 11.3 The main theorem.- 11.4 Operators with continuous coefficients - the degenerate case.- 11.5 Exercises.- Comments and references.- 12 Singular integral operators with bounded measurable coefficients.- 12.1 Singular operators with measurable coefficients in the space L2(?).- 12.2 Necessary conditions in the space L2(?).- 12.3 Lemmas.- 12.4 Singular operators with coefficients in ?p(?). Sufficient conditions.- 12.5 The Helson-Szegö theorem and its generalization.- 12.6 On the necessity of the condition a ? Sp.- 12.7 Extension of the class of coefficients.- 12.8 Exercises.- Comments and references.- 13 Exact constants in theorems on the boundedness of singular operators.- 13.1 Norm and quotient norm of the operator of singular integration.- 13.2 A second proof of Theorem 4.1 of Chapter 12.- 13.3 Norm and quotient norm of the operator S? on weighted spaces.- 13.4 Conditions for Fredholmness in spaces Lp(?, ?).- 13.5 Norms and quotient norm of the operator aI + bS?.- 13.6 Exercises.- Comments and references.- References.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Israel Gohberg,N. Krupnik,I. Gohberg\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3764327960\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783764327965\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Birkhauser\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/28\/1992\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 236\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.27lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.61h x 6.69w x 0.56d","brand":"Israel Gohberg","offers":[{"title":"Hardcover","offer_id":48136986820863,"sku":"9783764327965","price":99.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_1ea33dc5-dd97-4058-8ab5-f36bbbdf0f2d.jpg?v=1770165785","url":"https:\/\/www.whiterainbookhouse.com\/products\/one-dimensional-linear-singular-integral-equations-israel-gohberg-9783764327965","provider":"WR Book House","version":"1.0","type":"link"}