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Complete Second Order Linear Differential Equations in Hilbert Spaces
Alexander Ya. Shklyar
出版Birkhäuser, 2012-12-06
主題Mathematics / Functional AnalysisMathematics / Mathematical AnalysisMathematics / Calculus
ISBN30348918739783034891875
URLhttp://books.google.com.hk/books?id=a0EBCAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋Incomplete second order linear differential equations in Banach spaces as well as first order equations have become a classical part of functional analysis. This monograph is an attempt to present a unified systematic theory of second order equations y" (t) + Ay' (t) + By (t) = 0 including well-posedness of the Cauchy problem as well as the Dirichlet and Neumann problems. Exhaustive yet clear answers to all posed questions are given. Special emphasis is placed on new surprising effects arising for complete second order equations which do not take place for first order and incomplete second order equations. For this purpose, some new results in the spectral theory of pairs of operators and the boundary behavior of integral transforms have been developed. The book serves as a self-contained introductory course and a reference book on this subject for undergraduate and post- graduate students and research mathematicians in analysis. Moreover, users will welcome having a comprehensive study of the equations at hand, and it gives insight into the theory of complete second order linear differential equations in a general context - a theory which is far from being fully understood.