Introduction to Modern Analysis
Feb 2003 · Oxford Graduate Texts in Mathematics Buku 8 · OUP Oxford
e-Buku
448
Halaman
family_home
Layak
info
reportRating dan ulasan tidak disahkan Ketahui Lebih Lanjut
Perihal e-buku ini
This text is based on lectures given by the author at the advanced undergraduate and graduate levels in Measure Theory, Functional Analysis, Banach Algebras, Spectral Theory (of bounded and unbounded operators), Semigroups of Operators, Probability and Mathematical Statistics, and Partial Differential Equations. The first 10 chapters discuss theoretical methods in Measure Theory and Functional Analysis, and contain over 120 end of chapter exercises. The final two chapters apply theory to applications in Probability Theory and Partial Differential Equations. The Measure Theory chapters discuss the Lebesgue-Radon-Nikodym theorem which is given the Von Neumann Hilbert space proof. Also included are the relatively advanced topics of Haar measure, differentiability of complex Borel measures in Euclidean space with respect to Lebesgue measure, and the Marcinkiewicz' interpolation theorem for operators between Lebesgue spaces. The Functional Analysis chapters cover the usual material on Banach spaces, weak topologies, separation, extremal points, the Stone-Weierstrass theorem, Hilbert spaces, Banach algebras, and Spectral Theory for both bounded and unbounded operators. Relatively advanced topics such as the Gelfand-Naimark-Segal representation theorem and the Von Neumann double commutant theorem are included. The final two chapters deal with applications, where the measure theory and functional analysis methods of the first ten chapters are applied to Probability Theory and the Theory of Distributions and PDE's. Again, some advanced topics are included, such as the Lyapounov Central Limit theorem, the Kolmogoroff "Three Series theorem", the Ehrenpreis-Malgrange-Hormander theorem on fundamental solutions, and Hormander's theory of convolution operators. The Oxford Graduate Texts in Mathematics series aim is to publish textbooks suitable for graduate students in mathematics and its applications. The level of books may range from some suitable for advanced undergraduate courses at one end, to others of interest to research workers. The emphasis is on texts of high mathematical quality in active areas, particularly areas that are not well represented in the literature at present.
Berikan rating untuk e-Buku ini
Beritahu kami pendapat anda.
Maklumat pembacaan
Telefon pintar dan tablet
Pasang apl Google Play Books untuk Android dan iPad/iPhone. Apl ini menyegerak secara automatik dengan akaun anda dan membenarkan anda membaca di dalam atau luar talian, walau di mana jua anda berada.
Komputer riba dan komputer
Anda boleh mendengar buku audio yang dibeli di Google Play menggunakan penyemak imbas web komputer anda.
eReader dan peranti lain
Untuk membaca pada peranti e-dakwat seperti Kobo eReaders, anda perlu memuat turun fail dan memindahkan fail itu ke peranti anda. Sila ikut arahan Pusat Bantuan yang terperinci untuk memindahkan fail ke e-Pembaca yang disokong.
