Linear Operators: Spectral theory |
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Page 972
... that ( T ? Ke + p ) ( x ) = { x , p ] T- \ kes 2 6 R. Since characters have modulus
equal to unity , it follows from Plancherel's theorem that { u ( e + p ) } 2 = { u ( e ) }
Hence if ule ) < oo , we have proved that use + p ) is also finite and equals ule ) .
... that ( T ? Ke + p ) ( x ) = { x , p ] T- \ kes 2 6 R. Since characters have modulus
equal to unity , it follows from Plancherel's theorem that { u ( e + p ) } 2 = { u ( e ) }
Hence if ule ) < oo , we have proved that use + p ) is also finite and equals ule ) .
Page 1147
( b ) Any irreducible representation of G is equivalent to one of the
representations Rķa ) . ... complete set of representations is equal to the number
of distinct classes of G. The main aim of the representation theory of compact
groups is to display ...
( b ) Any irreducible representation of G is equivalent to one of the
representations Rķa ) . ... complete set of representations is equal to the number
of distinct classes of G. The main aim of the representation theory of compact
groups is to display ...
Page 1396
Then both deficiency indices of t are equal . Moreover , all the self adjoint
extensions of To ( t ) have the same set of non - isolated points , and this set is
equal to 0 ( t ) . Proof . The second assertion follows immediately from Theorem 5
and ...
Then both deficiency indices of t are equal . Moreover , all the self adjoint
extensions of To ( t ) have the same set of non - isolated points , and this set is
equal to 0 ( t ) . Proof . The second assertion follows immediately from Theorem 5
and ...
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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 |