Linear Operators: Spectral theory |
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Page 1224
Nelson Dunford, Jacob T. Schwartz. ( b ) If T , is symmetric then every symmetric
extension T , of Tı , and , in particular , every self adjoint extension of Tı , satisfies
TCT , C7 * CT * . Proof . If T , CT , and ye D ( 7 % ) , then ( « , 7 * y ) = ( Tgx , y ) ( T
...
Nelson Dunford, Jacob T. Schwartz. ( b ) If T , is symmetric then every symmetric
extension T , of Tı , and , in particular , every self adjoint extension of Tı , satisfies
TCT , C7 * CT * . Proof . If T , CT , and ye D ( 7 % ) , then ( « , 7 * y ) = ( Tgx , y ) ( T
...
Page 1236
Every closed symmetric extension of T is the restriction of 1 * 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 1 * 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
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
57 other sections not shown
Common terms and phrases
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 Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero
Bibliographic information
| Title | Linear Operators: Spectral theory Part 2 of Linear Operators, Nelson Dunford Volume 2 of Linear Operators: General Theory. Spectral Theory, Self Adjoint Operators in Hilbert Space. Spectral Operators. I. II. III, William George Bade Volume 2 of Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral Theory, Jacob T. Schwartz Volume 2; Volume 7 of Pure and applied mathematics : a series of texts and monographs Pure and applied mathematics Volume 7 of R.Courant L.Bers and J.J.Stoker Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Edition | reprint |
| Publisher | Interscience Publishers, 1988 |
| Original from | Pennsylvania State University |
| Digitized | 11 Oct 2011 |
| ISBN | 0470226382, 9780470226384 |
| Length | 1070 pages |
| Export Citation | BiBTeX EndNote RefMan |