Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1020
... matrix obtained by deleting the ith row and the jth column in ( a ,, ) . Then det ( A ) = a ,, A ,, and Σ - 1a , Aix = 0 if jk . Assuming that A is one - to - one , Cramer's rule for A - 1 asserts that the matrix of det ( 4 ) 4 - 1 ...
... matrix obtained by deleting the ith row and the jth column in ( a ,, ) . Then det ( A ) = a ,, A ,, and Σ - 1a , Aix = 0 if jk . Assuming that A is one - to - one , Cramer's rule for A - 1 asserts that the matrix of det ( 4 ) 4 - 1 ...
Page 1338
... matrix measure whose elements μ , are continuous with respect to a positive o - finite measure μ . If the matrix of densities { m } is defined by the equations μ1 , ( e ) = √ ̧m ,, ( 2 ) μ ( d2 ) , where e is any bounded Borel set ...
... matrix measure whose elements μ , are continuous with respect to a positive o - finite measure μ . If the matrix of densities { m } is defined by the equations μ1 , ( e ) = √ ̧m ,, ( 2 ) μ ( d2 ) , where e is any bounded Borel set ...
Page 1378
... matrix measure { p ;; } which by Corollary 21 must be the same as the matrix measure of Theorem 13. In particular , p1 , is unique . Thus , all that remains for us to prove is that if p ;; ( e ) for jk , then σ1 , ... , σ is a ...
... matrix measure { p ;; } which by Corollary 21 must be the same as the matrix measure of Theorem 13. In particular , p1 , is unique . Thus , all that remains for us to prove is that if p ;; ( e ) for jk , then σ1 , ... , σ is 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