Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1214
... real axis . Thus , if the function ƒ in vanishes outside S , the quantity ( V1f ) ( h ) = √ ̧ ̧ f ( s ) W ̧ ( 8 , λ ) v ( ds ) satisfies the inequalities S。| ( Vaƒ ) ( 2 ) \ 3μ . ( d2 ) ≤ \ / \ 2 S。{ Ss_ \ W . ( s , 2 ) | 2 v ( ds ) ...
... real axis . Thus , if the function ƒ in vanishes outside S , the quantity ( V1f ) ( h ) = √ ̧ ̧ f ( s ) W ̧ ( 8 , λ ) v ( ds ) satisfies the inequalities S。| ( Vaƒ ) ( 2 ) \ 3μ . ( d2 ) ≤ \ / \ 2 S。{ Ss_ \ W . ( s , 2 ) | 2 v ( ds ) ...
Page 1447
... real . Hence , by Theorem 5 , σ ( 7 ) is contained in the real axis . By the previous theorem the polynomial P ( t ) = Σ - 09 , ( it ) is real . If n is odd , this polynomial is of odd order . Hence , it converges to + ∞ as t ...
... real . Hence , by Theorem 5 , σ ( 7 ) is contained in the real axis . By the previous theorem the polynomial P ( t ) = Σ - 09 , ( it ) is real . If n is odd , this polynomial is of odd order . Hence , it converges to + ∞ as t ...
Page 1597
... real axis ( Hartman [ 16 ] ) . ( 22 ) In the interval ( 0 , a ] suppose that q is negative and non- decreasing , and that lim q ( t ) = ∞ . t → 0 Then the essential spectrum of t is void ( 6.27 , Sears [ 1 ] ) . ( 23 ) In the interval ...
... real axis ( Hartman [ 16 ] ) . ( 22 ) In the interval ( 0 , a ] suppose that q is negative and non- decreasing , and that lim q ( t ) = ∞ . t → 0 Then the essential spectrum of t is void ( 6.27 , Sears [ 1 ] ) . ( 23 ) In the interval ...
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