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 1703
... Problem Can the boundary value theory and the spectral theory of Chapter XIII be generalized to partial differential operators ? In the present section it will be seen that it can , at least for the class of elliptic partial ...
... Problem Can the boundary value theory and the spectral theory of Chapter XIII be generalized to partial differential operators ? In the present section it will be seen that it can , at least for the class of elliptic partial ...
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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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 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 PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero