Linear Operators: Spectral theory |
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Page 1626
J. Related theories . A number of other applications of linear analysis to the study of differential operators besides the spectral theory presented in the present chapter have recently received attention . Two of these theories seem ...
J. Related theories . A number of other applications of linear analysis to the study of differential operators besides the spectral theory presented in the present chapter have recently received attention . Two of these theories seem ...
Page 1628
A detailed exposition of this theory can be found in Levitan 1 ] . An approach to the study of differential operators in a Banach space of a more complex character than Hilbert space has been carried out by Feller [ 1 ] through [ 7 ] ...
A detailed exposition of this theory can be found in Levitan 1 ] . An approach to the study of differential operators in a Banach space of a more complex character than Hilbert space has been carried out by Feller [ 1 ] through [ 7 ] ...
Page 1813
On the theory of systems of linear differential equations in a one - dimensional domain , I , II . I. Mat . Sbornik N. S. 18 ( 60 ) , 305-328 ( 1946 ) . II . ibid . 21 ( 63 ) , 143-159 ( 1947 ) . ( Russian . English summary ) Math .
On the theory of systems of linear differential equations in a one - dimensional domain , I , II . I. Mat . Sbornik N. S. 18 ( 60 ) , 305-328 ( 1946 ) . II . ibid . 21 ( 63 ) , 143-159 ( 1947 ) . ( Russian . English summary ) Math .
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Contents
8 | 876 |
859 | 885 |
extensive presentation of applications of the spectral theorem | 911 |
Copyright | |
44 other sections not shown
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Common terms and phrases
additive adjoint adjoint operator algebra analytic assume basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero