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 - 19 ; 4x = 0 Σi = 1 if j #k . Assuming that A is one - to - one , Cramer's rule for A - 1 asserts that the matrix of det ( 4 ) 4 ...
... matrix obtained by deleting the ith row and the jth column in ( a ,, ) . Then det ( A ) = a ,, A ,, and Σ - 19 ; 4x = 0 Σi = 1 if j #k . Assuming that A is one - to - one , Cramer's rule for A - 1 asserts that the matrix of det ( 4 ) 4 ...
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 μ , ( e ) = fm ,, ( 2 ) μ ( d2 ) , where e is any bounded Borel set , then the ...
... 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 μ , ( e ) = fm ,, ( 2 ) μ ( d2 ) , where e is any bounded Borel set , then the ...
Page 1378
... matrix measure { p ,, } which by Corollary 21 must be the same as the matrix measure of Theorem 13. In particular , ôj is unique . Thus , all that remains for us to prove is that if p ,, ( e ) for jk , then σ1 , ... , σ is a determining ...
... matrix measure { p ,, } which by Corollary 21 must be the same as the matrix measure of Theorem 13. In particular , ôj is unique . Thus , all that remains for us to prove is that if p ,, ( e ) for jk , then σ1 , ... , σ is a determining ...
Contents
IX | 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 compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero