Linear Operators: Spectral theory |
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Page 1270
... problem of determining whether a given symmetric operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is affirmative , it is important ...
... problem of determining whether a given symmetric operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is affirmative , it is important ...
Page 1622
... problem . The wide application of the spectral theory of differential operators to a variety of problems in modern physics not only has shown a physical meaning for many of the mathematical notions , but has also raised some problems ...
... problem . The wide application of the spectral theory of differential operators to a variety of problems in modern physics not only has shown a physical meaning for many of the mathematical notions , but has also raised some problems ...
Page 1831
... problem of even order in the interval ( 0 , ∞ ) . Doklady Akad . Nauk SSSR ( N. S. ) 74 , 9–12 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ( 1951 ) . Solution of the inverse Sturm - Liouville problem . Doklady Akad . Nauk SSSR ( N. S. ) ...
... problem of even order in the interval ( 0 , ∞ ) . Doklady Akad . Nauk SSSR ( N. S. ) 74 , 9–12 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ( 1951 ) . Solution of the inverse Sturm - Liouville problem . Doklady Akad . Nauk SSSR ( N. S. ) ...
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