MARC Record from marc_columbia

LEADER: 05731cam a2200673Mi 4500
001 15131040
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006 m o d
007 cr cn|||||||||
008 180306s2014 flu ob 001 0 eng d
035 $a(OCoLC)on1027766596
035 $a(NNC)15131040
040 $aCRCPR$beng$erda$epn$cCRCPR$dOCLCO$dOCLCF$dOCLCQ$dOCLCO$dEBLCP$dYDX$dNLE$dUKMGB$dUWO$dOTZ$dAU@$dOCLCQ$dK6U$dOCLCO
015 $aGBB892505$2bnb
016 7 $a018866718$2Uk
019 $a1021301367
020 $a9781482288162$q(e-book)
020 $a1482288168
020 $z0415273560
020 $z9780415273565
024 7 $a10.1201/9781482288162$2doi
035 $a(OCoLC)1027766596$z(OCoLC)1021301367
037 $aTANDF_379083$bIngram Content Group
050 4 $aQC20.7.T45$bV533 2014
072 7 $aMAT037000$2bisacsh
072 7 $aMAT003000$2bisacsh
072 7 $aPBW$2bicssc
082 04 $a515.782
049 $aZCUA
100 1 $aVladimirov, V. S.,$eauthor.
245 10 $aMethods of the Theory of Generalized Functions /$cV.S. Vladimirov.
250 $aFirst edition.
264 1 $aBoca Raton, FL :$bCRC Press,$c2014.
300 $a1 online resource :$btext file, PDF
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
490 1 $aAnalytical methods and special functions ;$vv. 6
520 2 $a"This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences."--Provided by publisher.
505 0 $aCover; Half title; Analytical Methods and Special Functions; Title; Copyright; CONTENTS; Preface; Symbols and Definitions; CHAPTER 1 Generalized Functions and their Properties; 1. Test and Generalized Functions; 1.1. Introduction; 1.2. The space oftest functions 1>(0; 1.3. The space of generalized functions 1>'(0; 1.4. The completeness ofthe space of generalized functions 1>'(0; 1.5. The support of a generalized function; 1.6. Regular generalized functions.; 1.7. Measures; 1.8. Sochozki formulae; 1.9. Change of variables in generalized functions
505 8 $a1.10. Multiplication of generalized functions2. Differentiation of Generalized Functions; 2.1. Derivatives of generalized functions; 2.2. The antiderivative (primitive) of a generalized function; 2.3. Examples.; 2.4. The local structure of generalized functions; 2.5. Generalized functions with compact support; 2.6. Generalized functions with point support; 2.7. Generalized functions P(rr., lzl0 -- 1; 3. Direct Product of Generalized Functions; 3.1. The definition of a direct product; 3.2. The properties of a direct product; 3.3. Some applications
505 8 $a3.4. Generalized functions that are smooth with respect to some of the variables4. The Convolution of Generalized Functions; 4.1. The definition of convolution; 4.2. The properties of a conwlution; 4.3. The existence of a convolution; 4.4. Cones in 1Rn; 4.5. Convolution algebras V'(r+) and l>'(r; 4.6. Mean functions of generalized functions; 4.7. Multiplication of generalized functions; 4.8. Convolution as a continuous linear translationinvariant operator; 4.9. Some applications; 5. Tempered Generalized Functions; 5.1. The spaceS of test (rapidly decreasing) functions
505 8 $a5.2. The spaceS' of tempered generalized functions5.3. Examples oftempered generalized functions and elementary operations in S; 5.4. The structure of tempered generalized fUnctions; 5.5. The direct product of tempered generalized functions; 5.6. The convolution of tempered generalized fUnctions; 5.7 . Homogeneous generalized fUnctions; Chapter 2. Integral Transformations of Generalized Fuaetioas; 6. The Fourier Transform of Tempered Generalized Functions; 6.1. The Fourier transform of test functions in S; 6.2. The Fourier transform of tempered generalized functions
505 8 $a6.3. Properties of the Fourier transform6.4. The Fourier transform of generalized functions with compact support; 6.5. The Fourier transform of a convolution; 6.6. Examples; 6.7. The Mellin transform; 7. Fourier Series of Periodic Generalized Functions; 7.1. The definition and elementary properties of periodic generalized functions; 7.2. Fourier series of periodic generalized functions; 7.3. The convolution algebra 1; 7 .4. Examples; 8. Positive Definite Generalized Functions; 8.1. The definition and elementary properties of positive definite generalized fUnctions
504 $aIncludes bibliographical references and index.
650 0 $aMathematical analysis.
650 0 $aMathematics.
650 6 $aAnalyse mathématique.
650 6 $aMathématiques.
650 7 $amathematics.$2aat
650 7 $aapplied mathematics.$2aat
650 7 $aMathematical analysis.$2fast$0(OCoLC)fst01012068
650 7 $aMathematics.$2fast$0(OCoLC)fst01012163
655 0 $aElectronic books.
655 4 $aElectronic books.
776 08 $z9781482288162$z9780415273565
830 0 $aAnalytical methods and special functions ;$vv. 6.
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio15131040$zTaylor & Francis eBooks
852 8 $blweb$hEBOOKS