Linear Operators, Part 2 |
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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 1297
... complete under the norm | ƒ2 . As f1 ≤ If it follows from Theorem II.2.5 that the two norms are equivalent . The ... complete set of boundary values is a maximal linearly independent set of boundary values . Similarly , a complete set ...
... complete under the norm | ƒ2 . As f1 ≤ If it follows from Theorem II.2.5 that the two norms are equivalent . The ... complete set of boundary values is a maximal linearly independent set of boundary values . Similarly , a complete set ...
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 ) , I.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 ) , I.6.9 ( 20 ) Complete normed linear space . ( See B - space ) Complete orthonormal set , in ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 coefficients compact operator complex numbers constant 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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero