Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1070
... constant Kɛ such that ( 3 ) Swizz│ ¥ 3 ( u ) — ( Ko , * ¥ 2 ) ( u ) 1 + du < Kɛ √ § 22 ( w ) [ 1 + ε μ ( dw ) . 1 ε Since by Theorem 11 there exists a constant K such that ( 4 ) │Ko , * 42│1 + e ≤ Ke│Y2│1 + € ε { √ 1 ° r - ne ...
... constant Kɛ such that ( 3 ) Swizz│ ¥ 3 ( u ) — ( Ko , * ¥ 2 ) ( u ) 1 + du < Kɛ √ § 22 ( w ) [ 1 + ε μ ( dw ) . 1 ε Since by Theorem 11 there exists a constant K such that ( 4 ) │Ko , * 42│1 + e ≤ Ke│Y2│1 + € ε { √ 1 ° r - ne ...
Page 1154
... constant c , ( R ( 2 ) , ( 2 ) , ( 2 ) ) = c ( R , E , λ ) × ( R , E , ¿ ) . Since it is clear that = ( i ) 2 ( 2 ) ... constant c independent of E. This condition ( i ) , as is seen from Corollary III.11.6 , is a consequence of the ...
... constant c , ( R ( 2 ) , ( 2 ) , ( 2 ) ) = c ( R , E , λ ) × ( R , E , ¿ ) . Since it is clear that = ( i ) 2 ( 2 ) ... constant c independent of E. This condition ( i ) , as is seen from Corollary III.11.6 , is a consequence of the ...
Page 1176
... constants c1 are uniformly bounded . Similarly , multiplying each of the functions k , by a suitable positive constant c , we may suppose without loss of generality that each of the functions kn has total variation 1 ; here we have used ...
... constants c1 are uniformly bounded . Similarly , multiplying each of the functions k , by a suitable positive constant c , we may suppose without loss of generality that each of the functions kn has total variation 1 ; here we have used ...
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