Linear Operators, Part 2 |
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Page 1151
... remark inductively . 1 2 n Let F1 and F2 be disjoint closed sets in R. We select an open set G1 in R such that F1111 ... 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 . 1 2 n Let F1 and F2 be disjoint closed sets in R. We select an open set G1 in R such that F1111 ... 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 T1 following Definition 2.29 , the two linear functionals ƒ → ƒ ( 0 ) and ff ( 1 ) form a complete set of ... remarks following Definition 2.29 , the formal differential operator ( 1 / i ) ( d / dt ) , if considered to be defined ...
... remark T1 following Definition 2.29 , the two linear functionals ƒ → ƒ ( 0 ) and ff ( 1 ) form a complete set of ... remarks following Definition 2.29 , the formal differential operator ( 1 / i ) ( d / dt ) , if considered to be defined ...
Page 1472
... remark ( a ) made above , it then follows that for any two solutions f , g of λo , and a < c < b , we have τα 0 C = S¶ { ( ( x − 2 ) ƒ ) ( t ) g ( t ) − f ( t ) ( ( t — λ ) g ) ( t ) } dt = a = [ ' * { ( rf ) ( 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 τα 0 C = S¶ { ( ( x − 2 ) ƒ ) ( t ) g ( t ) − f ( t ) ( ( t — λ ) g ) ( t ) } dt = a = [ ' * { ( rf ) ( t ) g ( t ) − f ( t ) ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 coefficients compact operator complex numbers constant 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 Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero