Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 μ is called the measure of the ordered representation . The sets e , 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 μ is called the measure of the ordered representation . The sets e , will be called the ...
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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero