Linear Operators: Spectral theory |
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Page 906
... unitary if TT * T * T = I ; it is called self adjoint , symmetric or Hermitian if T = T * ; positive if it is self ... Unitary operators have a number of other characteristic proper- ties . For example , if U is unitary then ( x , y ) ...
... unitary if TT * T * T = I ; it is called self adjoint , symmetric or Hermitian if T = T * ; positive if it is self ... Unitary operators have a number of other characteristic proper- ties . For example , if U is unitary then ( x , y ) ...
Page 1146
... unitary 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 { U ,, ( g ) } . The ...
... unitary 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 { U ,, ( g ) } . The ...
Page 1148
... unitary matrices of determinant 1 ; or ( 3 ) The group SpU ( n ) of all 2n × 2n complex unitary matrices V such that [ Vx , Vy ] = [ x , y ] , where [ x , y ] is the non - singular bilinear form [ x , y ] X 1 Y 2Y1 X2 X3Y4 + ··· + X2n ...
... unitary matrices of determinant 1 ; or ( 3 ) The group SpU ( n ) of all 2n × 2n complex unitary matrices V such that [ Vx , Vy ] = [ x , y ] , where [ x , y ] is the non - singular bilinear form [ x , y ] X 1 Y 2Y1 X2 X3Y4 + ··· + X2n ...
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