Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1079
... eigenvalues of A ( each eigenvalue λ being repeated a number of times equal to the dimension of the range of E ( 2 ; A ) ) , then the eigenvalues of Ā ( m ) are λi , λig ... Aim λί 41 , 2 , ... , im being an arbitrary sequence of ...
... eigenvalues of A ( each eigenvalue λ being repeated a number of times equal to the dimension of the range of E ( 2 ; A ) ) , then the eigenvalues of Ā ( m ) are λi , λig ... Aim λί 41 , 2 , ... , im being an arbitrary sequence of ...
Page 1081
... eigenvalue of A , and to which there corresponds a non- negative eigenfunction . 39 Let A and B be n × n matrices and let { 2 , } be an enumeration of the eigenvalues of AB . Show that n Σ 2 , ≤ || A || || B || . i = 1 ( Hint : Put AB ...
... eigenvalue of A , and to which there corresponds a non- negative eigenfunction . 39 Let A and B be n × n matrices and let { 2 , } be an enumeration of the eigenvalues of AB . Show that n Σ 2 , ≤ || A || || B || . i = 1 ( Hint : Put AB ...
Page 1383
... eigen- values are consequently to be determined from the equation sin√λ = 0 . Consequently , in Case A , the eigenvalues 2 are the numbers of the form ( nл ) 2 , n ≥ 1 ; in Case C , the numbers { ( n + 1 ) л } 2 , n ≥ 0. In Case A ...
... eigen- values are consequently to be determined from the equation sin√λ = 0 . Consequently , in Case A , the eigenvalues 2 are the numbers of the form ( nл ) 2 , n ≥ 1 ; in Case C , the numbers { ( n + 1 ) л } 2 , n ≥ 0. In Case A ...
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