Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext)


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In addition, it contains a wealth of problems and exercises with solutions to guide the reader.

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Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations PDEs. Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics.

The English edition makes a welcome addition to this list. In fact I would recommend this over any other source to any beginning graduate student.

Its a bible for the field of research. At the end of each chapter the reader will find comments with further information, references, and historic remarks. In summary, the present textbook provides an excellent basis for a course on functional analysis plus a follow-up course on partial differential equations. It is well-written and I can wholeheartedly recommend it to both students and teachers. Teschl, Monatshefte fur Mathematik, Vol. The writing is lively, the material is diverse and maintains a strong unity.

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Functional analysis in applied mathematics and engineering - MathMods :: Joint MSc

I wholeheartedly recommend this book both as a textbook, as well as for independent study. It has seen translations into numerous languages and the Springer edition was especially anticipated, as it announced a number of practice exercises following each chapter. I can honestly say that it was well worth the wait. The text is a pleasure to read. I wholeheartedly recommend this book as both a textbook as well as for independent study.

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Functional Analysis, Sobolev Spaces and Partial Differential Equations

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Low convergence of a sequence in a Banach space, and weak-star convergence of a sequence in its dual. Low sequential compactness of the unit ball of a reflexive space. Theorems of the open application and of the closed graph. Topological supplement of a closed subspace, continuous projectors, inversible operators left or right.

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Introduction to the spectral theory of bounded linear operators in a Banach space. Spectre, solving set, resolving operator, spectral ray.

Possibly: spectral theory of compact operators. Sobolev spaces in dimension one.


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