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 § , 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 § , the centralizer ( 884 IX.5 IX . B - ALGEBRAS.
Page 1419
... result . On the interval [ $ i + 1 , mi + 1 ] , consider the two functions -f ( t ) and f1 ( t ) = + f ( 281 + 1 ... result . If q is negative for t sufficiently close to zero , then the preceding corollary applies to give the desired ...
... result . On the interval [ $ i + 1 , mi + 1 ] , consider the two functions -f ( t ) and f1 ( t ) = + f ( 281 + 1 ... result . If q is negative for t sufficiently close to zero , then the preceding corollary applies to give the desired ...
Page 1433
... result may be stated ; but here the basis for solutions of [ * ] may have a more complex form , involving logarithmic terms . We shall not give the details of this result here , but instead refer the reader to the excellent exposition ...
... result may be stated ; but here the basis for solutions of [ * ] may have a more complex form , involving logarithmic terms . We shall not give the details of this result here , but instead refer the reader to the excellent exposition ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero