Linear Operators: Spectral theory |
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Page 1236
A set of boundary conditions B , ( x ) = 0 , i = 1 , ... , k , is ; said to be symmetric if the equations B , ( x ) = B : ( y ) = 0 , i = 1 , ... , k , imply the equation { x , y } 0 . 26 LEMMA . Let T be an operator with finite ...
A set of boundary conditions B , ( x ) = 0 , i = 1 , ... , k , is ; said to be symmetric if the equations B , ( x ) = B : ( y ) = 0 , i = 1 , ... , k , imply the equation { x , y } 0 . 26 LEMMA . Let T be an operator with finite ...
Page 1238
Let T be a symmetric operator with finite deficiency indices whose sum is p . Let A , ... , A , be a complete set of boundary values for T , and let Xl , j = 1 Qi ; A ; Ā , be the bilinear form of Lemma 23 . A set of boundary conditions ...
Let T be a symmetric operator with finite deficiency indices whose sum is p . Let A , ... , A , be a complete set of boundary values for T , and let Xl , j = 1 Qi ; A ; Ā , be the bilinear form of Lemma 23 . A set of boundary conditions ...
Page 1272
Maximal symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is ...
Maximal symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is ...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero