Linear Operators: Spectral theory |
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Page 1011
... complete orthonormal set con- taining the element a 。 we clearly have T2 ≤ || T || 2 + ɛ and hence | T | ≤ || T || . Q.E.D. 3 COROLLARY . If T is in HS and { xa , a A } is any complete orthonormal set in § , then | T || = { Σ ( Txa ...
... complete orthonormal set con- taining the element a 。 we clearly have T2 ≤ || T || 2 + ɛ and hence | T | ≤ || T || . Q.E.D. 3 COROLLARY . If T is in HS and { xa , a A } is any complete orthonormal set in § , then | T || = { Σ ( Txa ...
Page 1147
... complete set of representations of a finite group is finite . DEFINITION : A class function on a compact group G is ... complete set of representations of G form a complete orthogonal basis for the space of class functions in L2 ( G ) ...
... complete set of representations of a finite group is finite . DEFINITION : A class function on a compact group G is ... complete set of representations of G form a complete orthogonal basis for the space of class functions in L2 ( G ) ...
Page 1903
... Complete and o - complete lattice , ( 43 ) Complete metric 1.6.15 ( 22 ) space , definition , I.6.5 ( 19 ) compact , properties , I.6.7 ( 20 ) , 1.6.9 ( 20 ) Complete normed linear space . ( See B - space ) Complete orthonormal set , in ...
... Complete and o - complete lattice , ( 43 ) Complete metric 1.6.15 ( 22 ) space , definition , I.6.5 ( 19 ) compact , properties , I.6.7 ( 20 ) , 1.6.9 ( 20 ) Complete normed linear space . ( See B - space ) Complete orthonormal set , in ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero