Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1116
... C. Let 71 , 7's be non - overlapping differentiable arcs having a limiting direction at infinity and suppose that no ... C2 . If we let Ap1 = y - p / 2p , then A is plainly self adjoint and A belongs to the class C ,, where r ( 1 - p / 2 ) = ...
... C. Let 71 , 7's be non - overlapping differentiable arcs having a limiting direction at infinity and suppose that no ... C2 . If we let Ap1 = y - p / 2p , then A is plainly self adjoint and A belongs to the class C ,, where r ( 1 - p / 2 ) = ...
Page 1154
... c , ( R ( 2 ) , ( 2 ) , ( 2 ) ) = c ( R , E , λ ) × ( R , E , ¿ ) . Since it is clear that = ( i ) 2 ( 2 ) ( E ) = c ... c2 ( 2 ) ( E ) for some constant c independent of E. This shows that 2 ( 2 ) ( AX B ) = cλ ( 2 ) ( BA ) for each pair of ...
... c , ( R ( 2 ) , ( 2 ) , ( 2 ) ) = c ( R , E , λ ) × ( R , E , ¿ ) . Since it is clear that = ( i ) 2 ( 2 ) ( E ) = c ... c2 ( 2 ) ( E ) for some constant c independent of E. This shows that 2 ( 2 ) ( AX B ) = cλ ( 2 ) ( BA ) for each pair of ...
Page 1308
... C2 ( f ) = 0 , and such that ƒ vanishes in a neighborhood of b . Similarly ... BA , ( ) = 0 , a2 + 82 0 , where A1 and A , are real boundary values which ... C , and D¡ , i pectively . = 1 , 2 , are real boundary values at a and b res ...
... C2 ( f ) = 0 , and such that ƒ vanishes in a neighborhood of b . Similarly ... BA , ( ) = 0 , a2 + 82 0 , where A1 and A , are real boundary values which ... C , and D¡ , i pectively . = 1 , 2 , are real boundary values at a and b res ...
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