Linear Operators: Spectral theory |
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Page 1379
... THEOREM . Let τ , T , A , 01 ,. on , etc. , be as in Theorem 18 . Then if , for j > k , the functions 0 ‡ ” ( 2 ) of Theorem 18 ( or , the functions 05 ( 2 ) of Theorem 18 ) may be extended to analytic functions defined on the whole ...
... THEOREM . Let τ , T , A , 01 ,. on , etc. , be as in Theorem 18 . Then if , for j > k , the functions 0 ‡ ” ( 2 ) of Theorem 18 ( or , the functions 05 ( 2 ) of Theorem 18 ) may be extended to analytic functions defined on the whole ...
Page 1591
... Theorem 11 was obtained by Weyl for operators of the second order , and extended by Glazman [ 1 ] . The trick used in Theorem 14 has been utilized by Wintner in some of his notes . Theorem 15 is due to Levinson [ 2 ] . The asymptotic ...
... Theorem 11 was obtained by Weyl for operators of the second order , and extended by Glazman [ 1 ] . The trick used in Theorem 14 has been utilized by Wintner in some of his notes . Theorem 15 is due to Levinson [ 2 ] . The asymptotic ...
Page 1904
... theorems , IV.15 Alexandroff theorem on conver- IV.9.15 gence of measures , ( 316 ) Arzelą theorem on continuous limits , IV.6.11 ( 268 ) Banach theorem for operators into space of measurable functions , IV.11.2–3 ( 332–333 ) Egoroff ...
... theorems , IV.15 Alexandroff theorem on conver- IV.9.15 gence of measures , ( 316 ) Arzelą theorem on continuous limits , IV.6.11 ( 268 ) Banach theorem for operators into space of measurable functions , IV.11.2–3 ( 332–333 ) Egoroff ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero