Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1058
... u - integrable on S. The Fubini theorem gives = and so ≤1 -log x1 | x | n − 1 dx = S q ( w ) μ ( do ) - S dr { S2 ( - log r | _ ( — logr — log ( w ) u ( dw ) } , -log | x1 dx + 2μ ( S ) S log log ( r ) dr , √ = 2 √ 451-1 and it ...
... u - integrable on S. The Fubini theorem gives = and so ≤1 -log x1 | x | n − 1 dx = S q ( w ) μ ( do ) - S dr { S2 ( - log r | _ ( — logr — log ( w ) u ( dw ) } , -log | x1 dx + 2μ ( S ) S log log ( r ) dr , √ = 2 √ 451-1 and it ...
Page 1085
... u - integrable function . Suppose that the number o1 of the preceding exercise is chosen to be 01 σ1 = √ § 4 ( 8 , 8 ) μ ( ds ) . = det ( R ) of the preceding exercise ( a ) Then the numbers d are given by the formulae do = 1 , d ...
... u - integrable function . Suppose that the number o1 of the preceding exercise is chosen to be 01 σ1 = √ § 4 ( 8 , 8 ) μ ( ds ) . = det ( R ) of the preceding exercise ( a ) Then the numbers d are given by the formulae do = 1 , d ...
Page 1341
... u . If { m } is the matrix of densities of p , with respect to μ , then there exist non- negative u - measurable functions q2 , i = 1 , ... , n , u - integrable over each bounded interval , and u - measurable functions a ,,, 1 ≤ i , j ...
... u . If { m } is the matrix of densities of p , with respect to μ , then there exist non- negative u - measurable functions q2 , i = 1 , ... , n , u - integrable over each bounded interval , and u - measurable functions a ,,, 1 ≤ i , j ...
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