Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1112
... formula and Cramer's formula for matrix inverses , we have d dz d d det ( A + B ) 2-0 = Σ Σ buπ ΣΥ i = 1 j = 1 = det ( 4 ) tr ( A - 1B ) , where Yij denotes the cofactor of the element a ,, of the matrix A. Substituting A = I + T and ...
... formula and Cramer's formula for matrix inverses , we have d dz d d det ( A + B ) 2-0 = Σ Σ buπ ΣΥ i = 1 j = 1 = det ( 4 ) tr ( A - 1B ) , where Yij denotes the cofactor of the element a ,, of the matrix A. Substituting A = I + T and ...
Page 1288
... formula was established for the case f , ge C " ( I ) . However , the arguments are equally valid for f , ge H ( I ) . Q.E.D. It will be convenient for what follows to record other situations in which Green's formula is valid but where ...
... formula was established for the case f , ge C " ( I ) . However , the arguments are equally valid for f , ge H ( I ) . Q.E.D. It will be convenient for what follows to record other situations in which Green's formula is valid but where ...
Page 1363
... formula 1 ρλε E ( ( 21 , 22 ) ) f -- lim lim 2πί . + 0-3 0-8 21 + 8 [ R ( 1 - iɛ ; T ) -R ( λ + iɛ ; T ) ] fdλ . The problem we face is that of passing from this latter formula in- volving the resolvent to a formula involving the ...
... formula 1 ρλε E ( ( 21 , 22 ) ) f -- lim lim 2πί . + 0-3 0-8 21 + 8 [ R ( 1 - iɛ ; T ) -R ( λ + iɛ ; T ) ] fdλ . The problem we face is that of passing from this latter formula in- volving the resolvent to a formula involving the ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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