LEADER 04281nam 2200673Ia 450 001 9911019786603321 005 20200520144314.0 010 $a9786613306180 010 $a9781283306188 010 $a1283306182 010 $a9781118032510 010 $a1118032519 010 $a9781118030752 010 $a1118030753 035 $a(CKB)2550000000056668 035 $a(EBL)694489 035 $a(OCoLC)778616737 035 $a(SSID)ssj0000554856 035 $a(PQKBManifestationID)11308412 035 $a(PQKBTitleCode)TC0000554856 035 $a(PQKBWorkID)10530125 035 $a(PQKB)10027645 035 $a(MiAaPQ)EBC694489 035 $a(PPN)169654443 035 $a(Perlego)2784547 035 $a(EXLCZ)992550000000056668 100 $a19950502d1996 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Hilbert transform of Schwartz distributions and applications /$fJ.N. Pandey 210 $aNew York $cJohn Wiley$dc1996 215 $a1 online resource (284 p.) 225 1 $aPure and applied mathematics 300 $aDescription based upon print version of record. 311 08$a9780471033738 311 08$a0471033731 320 $aIncludes bibliographical references (p. 249-253) and indexes. 327 $aThe Hilbert Transform of Schwartz Distributions and Applications; CONTENTS; Preface; 1. Some Background; 1.1. Fourier Transforms and the Theory of Distributions; 1.2. Fourier Transforms of L2 Functions; 1.2.1. Fourier Transforms of Some Well-known Functions; 1.3. Convolution of Functions; 1.3.1. Differentiation of the Fourier Transform; 1.4. Theory of Distributions; 1.4.1. Topological Vector Spaces; 1.4.2. Locally Convex Spaces; 1.4.3. Schwartz Testing Function Space: Its Topology and Distributions; 1.4.4. The Calculus of Distribution; 1.4.5. Distributional Differentiation 327 $a1.5. Primitive of Distributions1.6. Characterization of Distributions of Compact Supports; 1.7. Convolution of Distributions; 1.8. The Direct Product of Distributions; 1.9. The Convolution of Functions; 1.10. Regularization of Distributions; 1.11. The Continuity of the Convolution Process; 1.12. Fourier Transforms and Tempered Distributions; 1.12.1. The Testing Function Space S(Rn); 1.13. The Space of Distributions of Slow Growth S'(Rn); 1.14. A Boundedness Property of Distributions of Slow Growth and Its Structure Formula; 1.15. A Characterization Formula for Tempered Distributions 327 $a1.16. Fourier Transform of Tempered Distributions1.17. Fourier Transform of Distributions in D'(Rn); Exercises; 2. The Riemann-Hilbert Problem; 2.1. Some Corollaries on Cauchy Integrals; 2.2. Riemann's Problem; 2.2.1. The Hilbert Problem; 2.2.2. Riemann-Hilbert Problem; 2.3. Carleman's Approach to Solving the Riemann-Hilbert Problem; 2.4. The Hilbert Inversion Formula for Periodic Functions; 2.5. The Hilbert Transform on the Real Line; 2.6. Finite Hilbert Transform as Applied to Aerofoil Theories; 2.7. The Riemann-Hilbert Problem Applied to Crack Problems 327 $a4.5. The Intrinsic Definition of the Space H(D) 330 $aThis book provides a modern and up-to-date treatment of the Hilbert transform of distributions and the space of periodic distributions. Taking a simple and effective approach to a complex subject, this volume is a first-rate textbook at the graduate level as well as an extremely useful reference for mathematicians, applied scientists, and engineers.The author, a leading authority in the field, shares with the reader many new results from his exhaustive research on the Hilbert transform of Schwartz distributions. He describes in detail how to use the Hilbert transform to solve theoretic 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aHilbert transform 606 $aSchwartz distributions 615 0$aHilbert transform. 615 0$aSchwartz distributions. 676 $a515/.782 700 $aPandey$b J. N$01842740 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019786603321 996 $aThe Hilbert transform of Schwartz distributions and applications$94422951 997 $aUNINA