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 { U1 , ( 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 { U1 , ( 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 ] X1Y2Y1 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 ] X1Y2Y1 X2 + x3Y4 + ··· + x2n ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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