000 04443nam a22005415i 4500
001 978-0-8176-4442-0
003 DE-He213
005 20251006084434.0
007 cr nn 008mamaa
008 100301s2005 xxu| s |||| 0|eng d
020 _a9780817644420
020 _a99780817644420
024 7 _a10.1007/0-8176-4442-3
_2doi
082 0 4 _a515
_223
100 1 _aKnapp, Anthony W.
_eauthor.
245 1 0 _aAdvanced Real Analysis
_h[electronic resource] :
_bAlong with a companion volume Basic Real Analysis /
_cby Anthony W. Knapp.
264 1 _aBoston, MA :
_bBirkhäuser Boston,
_c2005.
300 _aXXIV, 468 p. 6 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 _ato Boundary-Value Problems -- Compact Self-Adjoint Operators -- Topics in Euclidean Fourier Analysis -- Topics in Functional Analysis -- Distributions -- Compact and Locally Compact Groups -- Aspects of Partial Differential Equations -- Analysis on Manifolds -- Foundations of Probability.
520 _aBasic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features of Advanced Real Analysis: * Develops Fourier analysis and functional analysis with an eye toward partial differential equations * Includes chapters on Sturm-Liouville theory, compact self-adjoint operators, Euclidean Fourier analysis, topological vector spaces and distributions, compact and locally compact groups, and aspects of partial differential equations * Contains chapters about analysis on manifolds and foundations of probability * Proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * Includes many examples and nearly two hundred problems, and a separate 45-page section gives hints or complete solutions for most of the problems * Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds Advanced Real Analysis requires of the reader a first course in measure theory, including an introduction to the Fourier transform and to Hilbert and Banach spaces. Some familiarity with complex analysis is helpful for certain chapters. The book is suitable as a text in graduate courses such as Fourier and functional analysis, modern analysis, and partial differential equations. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician.
650 0 _aMATHEMATICS.
650 0 _aGLOBAL ANALYSIS (MATHEMATICS).
650 0 _aFOURIER ANALYSIS.
650 0 _aFUNCTIONAL ANALYSIS.
650 0 _aGLOBAL ANALYSIS.
650 0 _aDIFFERENTIAL EQUATIONS, PARTIAL.
650 0 _aDISTRIBUTION (PROBABILITY THEORY).
650 1 4 _aMATHEMATICS.
650 2 4 _aANALYSIS.
650 2 4 _aFUNCTIONAL ANALYSIS.
650 2 4 _aFOURIER ANALYSIS.
650 2 4 _aPARTIAL DIFFERENTIAL EQUATIONS.
650 2 4 _aGLOBAL ANALYSIS AND ANALYSIS ON MANIFOLDS.
650 2 4 _aPROBABILITY THEORY AND STOCHASTIC PROCESSES.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817643829
830 0 _aCornerstones
856 4 0 _uhttp://dx.doi.org/10.1007/0-8176-4442-3
_zVer el texto completo en las instalaciones del CICY
912 _aZDB-2-SMA
942 _2ddc
_cER
999 _c59640
_d59640