Advanced Real Analysis: With a Companion Volume 'Basic Real by Anthony W. Knapp

By Anthony W. Knapp

complex genuine research systematically develops these techniques and instruments in actual research which are important to each mathematician, even if natural or utilized, aspiring or confirmed. in addition to a spouse quantity simple actual research (available individually or jointly as a Set), those works current a complete remedy with a world view of the topic, emphasizing the connections among genuine research and different branches of arithmetic. complex actual research calls for of the reader a primary path in degree concept, together with an advent to the Fourier rework and to Hilbert and Banach areas. a few familiarity with advanced research is beneficial for definite chapters. The e-book is acceptable as a textual content in graduate classes corresponding to Fourier and practical research, smooth research, and partial differential equations. since it specializes in what each younger mathematician must find out about genuine research, the ebook is perfect either as a path textual content and for self-study, specifically for graduate scholars getting ready for qualifying examinations. Its scope and technique will attract teachers and professors in approximately all components of natural arithmetic, in addition to utilized mathematicians operating in analytic components resembling records, mathematical physics, and differential equations. certainly, the readability and breadth of complex genuine research make it a welcome boost to the non-public library of each mathematician.

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