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Applied functional analysis. Exercises by Bernard Cornet and Jean-Michel Lasry. Transl. by Carole Labrousse. 2nd ed. (English) Zbl 0946.46001
The first English edition of this book appeared in 1979, cf. Zbl 0424.46001. The second edition has made some additions and some deletions. Its contents are best described as introduction to functional analysis with applications. All the functional analysis centres around the theory of Hilbert spaces of various sorts introduced in the first five chapters. The next four chapters specialize the theory to study Sobolev spaces. The last part, made up of seven chapters, consists of diverse applications: convex analysis, spectral theory, boundary value problems, Nagumo’s theorem (a theorem in the theory of ordinary differential equations with varied applications), first-order partial differential equations. Many areas of application are alluded to although not actually developed.

MSC:
46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
47-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
47A10 Spectrum, resolvent
35J25 Boundary value problems for second-order elliptic equations
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