Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1151
... remark inductively . 2 n Let F1 and F2 be disjoint closed sets in R. We select an open set G , in R such that FOKCG ... remarked that this theorem was proved for compact groups in Theorem 1.1 , and that the only use XI.11.3 1151 NOTES ...
... remark inductively . 2 n Let F1 and F2 be disjoint closed sets in R. We select an open set G , in R such that FOKCG ... remarked that this theorem was proved for compact groups in Theorem 1.1 , and that the only use XI.11.3 1151 NOTES ...
Page 1381
... remark following Definition 2.29 , the two linear functionals f → f ( 0 ) and ƒ → ƒ ( 1 ) form a complete set of ... remarks following Definition 2.29 , the formal differential operator ( 1 / i ) ( d / dt ) , if considered to be ...
... remark following Definition 2.29 , the two linear functionals f → f ( 0 ) and ƒ → ƒ ( 1 ) form a complete set of ... remarks following Definition 2.29 , the formal differential operator ( 1 / i ) ( d / dt ) , if considered to be ...
Page 1472
... remark ( a ) made above , it then follows that for any two solutions f , g of λo , and a < c < b , we have τσ = 0 = [ ° { ( ( x − h ) f ) ( t ) g ( t ) − f ( t ) ( ( r — λ ) g ) ( t ) } dt = a = S¶ { ( xf ) ( t ) g ( t ) − f ( t ) ...
... remark ( a ) made above , it then follows that for any two solutions f , g of λo , and a < c < b , we have τσ = 0 = [ ° { ( ( x − h ) f ) ( t ) g ( t ) − f ( t ) ( ( r — λ ) g ) ( t ) } dt = a = S¶ { ( xf ) ( t ) g ( t ) − f ( t ) ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise 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 L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero