000 04026nam a22005295i 4500
001 978-0-8176-4675-2
003 DE-He213
005 20140220084457.0
007 cr nn 008mamaa
008 100806s2010 xxu| s |||| 0|eng d
020 _a9780817646752
_9978-0-8176-4675-2
024 7 _a10.1007/978-0-8176-4675-2
_2doi
050 4 _aQA401-425
072 7 _aPBKJ
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a511.4
_223
100 1 _aDuistermaat, J.J.
_eauthor.
245 1 0 _aDistributions
_h[electronic resource] :
_bTheory and Applications /
_cby J.J. Duistermaat, J.A.C. Kolk.
250 _a1.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2010.
300 _aXVI, 445p. 41 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aCornerstones
505 0 _aMotivation -- Test Functions -- Distributions -- Differentiation of Distributions -- Convergence of Distributions -- Taylor Expansion in Several Variables -- Localization -- Distributions with Compact Support -- Multiplication by Functions -- Transposition: Pullback and Pushforward -- Convolution of Distributions -- Fundamental Solutions -- Fractional Integration and Differentiation -- Fourier Transform -- Distribution Kernels -- Fourier Series -- Fundamental Solutions and Fourier Transform -- Supports and Fourier Transform -- Sobolev Spaces -- Appendix: Integration -- Solutions to Selected Problems.
520 _aThis textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. Throughout the book, methods are developed to deal with formal calculations involving functions, series, and integrals that cannot be mathematically justified within the classical framework. Key features: • Many examples, exercises, hints, and solutions guide the reader throughout the text. • Includes an introduction to distributions, differentiation, convergence, convolution, the Fourier transform, and spaces of distributions having special properties. • Original proofs, which may be difficult to locate elsewhere, are given for many well-known results. • The Fourier transform is transparently treated and applied to provide a new proof of the Kernel Theorem, which in turn is used to efficiently derive numerous important results. • The systematic use of pullback and pushforward introduces concise notation. • Emphasizes the role of symmetry in obtaining short arguments and investigates distributions that are invariant under the actions of various groups of transformations. Distributions: Theory and Applications is aimed at advanced undergraduates and graduate students in mathematics, theoretical physics, and engineering, who will find this textbook a welcome introduction to the subject, requiring only a minimal mathematical background. The work may also serve as an excellent self-study guide for researchers who use distributions in various fields.
650 0 _aMathematics.
650 0 _aFourier analysis.
650 0 _aDifferential Equations.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aApproximations and Expansions.
650 2 4 _aApplications of Mathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aFourier Analysis.
650 2 4 _aOrdinary Differential Equations.
700 1 _aKolk, J.A.C.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817646721
830 0 _aCornerstones
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-4675-2
912 _aZDB-2-SMA
999 _c109901
_d109901