Linear Operators: Spectral theory |
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Page 884
... results of this theory we present only a single result , due to von Neu- mann [ 2 ] , in this direction . If A is a collection of bounded linear opera- tors in a Hilbert space H , the centralizer ( 884 IX.5 IX . B - ALGEBRAS.
... results of this theory we present only a single result , due to von Neu- mann [ 2 ] , in this direction . If A is a collection of bounded linear opera- tors in a Hilbert space H , the centralizer ( 884 IX.5 IX . B - ALGEBRAS.
Page 1156
... result , which is dual to Theorem 8 . ∞ 9 THEOREM . If R is a discrete Abelian group , its character group R is compact . Ris The results of Sections 3 and 4 carry over for the case of discrete groups and many of them , for example ...
... result , which is dual to Theorem 8 . ∞ 9 THEOREM . If R is a discrete Abelian group , its character group R is compact . Ris The results of Sections 3 and 4 carry over for the case of discrete groups and many of them , for example ...
Page 1419
... result . On the interval [ 8 + 1 , mi + 1 ] , consider the two functions −f ( t ) and f1 ( t ) = + f ( 28 ; + 1 - t ) ... result . If q is negative for t sufficiently close to zero , then the preceding corollary applies to give the ...
... result . On the interval [ 8 + 1 , mi + 1 ] , consider the two functions −f ( t ) and f1 ( t ) = + f ( 28 ; + 1 - t ) ... result . If q is negative for t sufficiently close to zero , then the preceding corollary applies to give the ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero