{"product_id":"the-mellin-transformation-and-fuchsian-z-szmydt-9780792316831","title":"The Mellin Transformation and Fuchsian Type Partial Differential Equations","description":"I. Introduction.-  1. Terminology and notation.-  2. Elementary facts on complex topological vector spaces.- 1. Multinormed complex vector spaces and their duals.- 2. Inductive and projective limits.- 3. Subspaces. The Hahn-Banach theorem.- Exercise.-  3. A review of basic facts in the theory of distributions.- 1. Spaces DK and (DK)1.- 2. Spaces D(A) and D'(A).- 3. Spaces S and S1.- 4. Spaces E and E1.- 5. Substitution in distributions. Homogeneous distributions.- 6. Classical order of a distribution and extendibility theorems for distributions.- 7. Convolution of distributions.- 8. Tensor product of distributions.- Exercises.- II. Mellin distributions and the Mellin transformation.-  4. The Fourier and the Fourier-Mellin transformations.- 1. The Fourier transformation in S1.- 2. The Fourier-Mellin transformation in the space of Mellin distributions with support in % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb % qegWuDJLgzHbIrHHhaiuqacqWFsbGufaqabeGabaaabaqcLbqacGao % 4pOBaaGcbaqcLbqacWaGaI7-q8VHRaWkaaaaaa!450D!$$ R\\begin{array}{*{20}{c}} n \\\\ + \\end{array} $$.- Exercises.-  5. The spaces of Mellin distributions with support in a polyinterval.- 1. Spaces Ma, ((0, t]) and M1a ((0, t]).- 2. Spaces M(?) ((0, t]) and M1(?) ((0, t]).- Exercises.-  6. Operations of multiplication and differentiation in the space of Mellin distributions.- 1. Multiplication and differentiation in Ma, M(?) and their duals.- 2. Mellin multipliers.- Exercises.-  7. The Mellin transformation in the space of Mellin distributions.- 1. The Mellin transformation in the space of Mellin distributions and its relations with the Fourier-Laplace transformation.- 2. Examples of Mellin transforms of some functions.- 3. Mellin transforms of certain cut-off functions.- 3.1. One-dimensional smooth cut-off functions.- 3.2. n-Dimensional smooth cut-off functions with a parameter.- Exercises.-  8. The structure of Mellin distributions.- 1. Characterizations of Mellin distributions.- 2. Substitution in a Mellin distribution.- 3. Mellin order of a Mellin distribution.- Exercises.-  9. Paley-Wiener type theorems for the Mellin transformation.- Exercises.-  10. Mellin transforms of cut-off functions (continued).- 1. Conical cut-off functions.- 2. The K-inequalities.- 3. The \"tangent cones\" ?K and related cut-off functions.- 4. Further investigation of the Mellin transform of a conical cut-off function.- Exercises.-  11. Important subspaces of Mellin distributions.- 1. Subspaces % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaacI % cacaWG4bWaaSaaaeaacaWGKbaabaGaamizaiaadIhaaaGaaiykaiaa % dwhacqGH9aqpcaWGMbaaaa!3EE9!$$ P(x\\frac{d}{{dx}})u = f $$.- 2. Subspaces SPr(s, s1 ) of Mellin distributions.- 3. Spaces M(? ?) and Zd(? ?) of distributions with continuous radial asymptotics.- Exercises.-  12. The modified Cauchy transformation.- 1. Modified Cauchy and Hilbert transformations in dimension 1.- 2. The case with parameters.- Exercises.- III. Fuchsian type singular operators.-  13. Fuchsian type ordinary differential operators.- 1. Asymptotic expansions.- 2. The equation % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamytamXvP5 % wqonvsaeHbmv3yPrwyGmvyUnhaiuGajugOaiadaciaaW3--Leajjad % acigaa3--nhaZPWaiaiG47p6-V\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Z. Szmydt, Bogdan Ziemian, B. Ziemian\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0792316835\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780792316831\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Kluwer Academic Publishers\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 03\/31\/1992\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 240\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.13lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.56d","brand":"Z. Szmydt","offers":[{"title":"Hardcover","offer_id":47202165719295,"sku":"9780792316831","price":109.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_6477a860-f130-43b0-8cec-a58bfa01c96d.jpg?v=1756819819","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-mellin-transformation-and-fuchsian-z-szmydt-9780792316831","provider":"WR Book House","version":"1.0","type":"link"}