Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1079
... eigenvalues of A ( each eigenvalue being repeated a number of times equal to the dimension of the range of E ( 2 ; A ) ) , then the eigenvalues of A ( m ) are i1 , i2 , . . Ai , λin ... Aim λες λί im being an arbitrary sequence of ...
... eigenvalues of A ( each eigenvalue being repeated a number of times equal to the dimension of the range of E ( 2 ; A ) ) , then the eigenvalues of A ( m ) are i1 , i2 , . . Ai , λin ... Aim λες λί 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 { 1 , } be an enumeration of the eigenvalues of AB . Show that n Σ λ ≤ || A || || B || . i = 1 ( Hint : Put AB in ...
... eigenvalue of A , and to which there corresponds a non- negative eigenfunction . 39 Let A and B be n × n matrices and let { 1 , } be an enumeration of the eigenvalues of AB . Show that n Σ λ ≤ || A || || B || . i = 1 ( Hint : Put AB in ...
Page 1383
... eigen- values are consequently to be determined from the equation sin √ = 0 . Consequently , in Case A , the eigenvalues 2 are the numbers of the form ( në ) 2 , n ≥ 1 ; in Case C , the numbers { ( n + 1 ) π } 2 , n ≥ 0. In Case A ...
... eigen- values are consequently to be determined from the equation sin √ = 0 . Consequently , in Case A , the eigenvalues 2 are the numbers of the form ( në ) 2 , n ≥ 1 ; in Case C , the numbers { ( n + 1 ) π } 2 , n ≥ 0. In Case A ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero