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100   $a20180709d2018      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 12$aA Course in Functional Analysis and Measure Theory /$fby Vladimir Kadets
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (XXII, 539 p.) 
225 1 $aUniversitext,$x0172-5939
311   $a3-319-92003-0 
327   $aIntroduction -- Chapter 1. Metric and topological spaces -- Chapter 2. Measure theory -- Chapter 3. Measurable functions -- Chapter 4. The Lebesgue integral -- Chapter 5. Linear spaces, linear functionals, and the Hahn-Banach theorem -- Chapter 6. Normed spaces -- Chapter 7. Absolute continuity of measures and functions. Connection between derivative and integral -- Chapter 8. The integral on C(K) -- Chapter 9. Continuous linear functionals -- Chapter 10. Classical theorems on continuous operators -- Chapter 11. Elements of spectral theory of operators. Compact operators -- Chapter 12. Hilbert spaces -- Chapter 13. Functions of an operator -- Chapter 14. Operators in Lp -- Chapter 15. Fixed-point theorems and applications -- Chapter 16. Topological vector spaces -- Chapter 17. Elements of duality theory -- Chapter 18. The Krein-Milman theorem and applications -- References. Index.
330   $aWritten by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.
410  0$aUniversitext,$x0172-5939
606   $aFunctional analysis
606   $aMeasure theory
606   $aOperator theory
606   $aFunctions of real variables
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120
606   $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139
606   $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171
615  0$aFunctional analysis.
615  0$aMeasure theory.
615  0$aOperator theory.
615  0$aFunctions of real variables.
615 14$aFunctional Analysis.
615 24$aMeasure and Integration.
615 24$aOperator Theory.
615 24$aReal Functions.
676   $a515.7
700   $aKadets$b Vladimir$4aut$4http://id.loc.gov/vocabulary/relators/aut$059669
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300099803321
996   $a???? ??????????????? ???????$91779199
997   $aUNINA