Linear Operators, Part 2 |
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Page 1224
( b ) If T , is symmetric then every symmetric extension T , of Tj and , in particular ,
every self adjoint extension of Tı , satisfies T , CT , C7 * CT * Proof . If T , CT , and
ye D ( T * ) , then ( x , 7 * y ) = ( T2x , y ) = ( 1 x , y ) for any xED ( T ) . Hence y eD ...
( b ) If T , is symmetric then every symmetric extension T , of Tj and , in particular ,
every self adjoint extension of Tı , satisfies T , CT , C7 * CT * Proof . If T , CT , and
ye D ( T * ) , then ( x , 7 * y ) = ( T2x , y ) = ( 1 x , y ) for any xED ( T ) . Hence y eD ...
Page 1236
Every closed symmetric extension of T is the restriction of T ' * to the subspace of
D ( T * ) determined by a symmetric family of boundary conditions , B ; ( x ) = 0 , i =
1 , . . . , k . Conversely , every such restriction T , of T * is a closed symmetric ...
Every closed symmetric extension of T is the restriction of T ' * to the subspace of
D ( T * ) determined by a symmetric family of boundary conditions , B ; ( x ) = 0 , i =
1 , . . . , k . Conversely , every such restriction T , of T * is a closed symmetric ...
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 one which has no
proper ...
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 one which has no
proper ...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
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additive adjoint operator 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 derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function give 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
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Bibliographic information
| Title | Linear Operators, Part 2 Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics Issue 7 of Pure and applied mathematics; a series of monographs and textbooks |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1963 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0471226386, 9780471226383 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |