Linear Operators: Spectral theory |
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Page 1146
... representations . If such a representation acts in a finite dimensional space E " , then introducing a basis for E " , we may regard the representation as being described by a set of unitary matrices { U1 , ( g ) } . The individual ...
... representations . If such a representation acts in a finite dimensional space E " , then introducing a basis for E " , we may regard the representation as being described by a set of unitary matrices { U1 , ( g ) } . The individual ...
Page 1147
... representation of G is equivalent to one of the representations R ( a ) . COROLLARY : If G is a compact topological group satisfying the second axiom of countability , and G is not a finite set , then any complete set of representations ...
... representation of G is equivalent to one of the representations R ( a ) . COROLLARY : If G is a compact topological group satisfying the second axiom of countability , and G is not a finite set , then any complete set of representations ...
Page 1217
... representation of a Hilbert space relative to a self adjoint operator T in is said to be an ordered representation of § relative to T. The measure u is called the measure of the ordered representation . The sets en will be called the ...
... representation of a Hilbert space relative to a self adjoint operator T in is said to be an ordered representation of § relative to T. The measure u is called the measure of the ordered representation . The sets en will be called the ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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