Spectral Theory of Ordinary Differential Operators

These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces.

Spectral Theory of Ordinary Differential Operators

These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.

More Books:

Spectral Theory of Ordinary Differential Operators
Language: en
Pages: 304
Authors: Joachim Weidmann
Categories: Mathematics
Type: BOOK - Published: 2006-11-15 - Publisher: Springer

These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions
Spectral Theory of Non-self-adjoint Two-point Differential Operators
Language: en
Pages: 252
Authors: John Locker
Categories: Mathematics
Type: BOOK - Published: 2000 - Publisher: American Mathematical Soc.

This monograph develops the spectral theory of an $n$th order non-self-adjoint two-point differential operator $L$ in the Hilbert space $L^2[0,1]$. The mathematical foundation is laid in the first part, where the spectral theory is developed for closed linear operators and Fredholm operators. An important completeness theorem is established for the
Partial Differential Equations VII
Language: en
Pages: 274
Authors: M.A. Shubin
Categories: Mathematics
Type: BOOK - Published: 2013-03-09 - Publisher: Springer Science & Business Media

This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum".
Spectral Theory of Differential Operators
Language: en
Pages: 390
Authors: V.A. Il'in, Vladimir Aleksandrovič Ilʹin, Vladimir Aleksandrovič Il'in
Categories: Gardening
Type: BOOK - Published: 1995-08-31 - Publisher: Springer

In this fully-illustrated textbook, the author examines the spectral theory of self-adjoint elliptic operators. Chapters focus on the problems of convergence and summability of spectral decompositions about the fundamental functions of elliptic operators of the second order. The author's work offers a novel method for estimation of the remainder term
Spectral Theory of Differential Operators
Language: en
Pages: 383
Authors: I.W. Knowles, R.T. Lewis
Categories: Mathematics
Type: BOOK - Published: 1981-01-01 - Publisher: Elsevier

Spectral Theory of Differential Operators