Bøger i Birkhauser Advanced Texts / Basler Lehrbucher serien

This book studies observation and control operators for linear systems where the free evolution of the state can be described by an operator semigroup on a Hilbert space. It includes a large number of examples coming mostly from partial differential equations.

This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work.

The analysis of Euclidean space is well-developed. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. The normal and tangent bundles become part of the language of classical analysis when that analysis is done on a domain.

"This book covers some of the main aspects of nonlinear analysis. I recommend this book to anyone interested in the main and essential concepts of nonlinear analysis as well as the relevant methodologies and applications."

Key topics in the theory of real analytic functions are covered in this text,and are rather difficult to pry out of the mathematics literature.; alternative characterizations of real analytic functions, surjectivity of partial differential operators, And the Weierstrass preparation theorem.

Chapters 1-6 give the function-theoretic background to Hardy Classes and Operator Theory, Oxford Mathematical Monographs, Oxford University Press, New York, 1985. The theory of Hardy and Nevanlinna classes is derived from proper ties of harmonic majorants of subharmonic functions (Chapters 3 and 4).

This book provides proofs of the asymptotic behavior of solutions to various important cases of linear and nonlinear problems in the theory of elliptic and parabolic partial differential equations. They will motivate and enable the reader to apply the theory to other problems in partial differential equations.