Linear Operators: Spectral theory |
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Page 1591
... second order : the general result has been obtained by Naimark [ 5 ] . Section 7. Most of the results given in this section are found in the literature only in the special case of operators of second order . Some of the theorems have ...
... second order : the general result has been obtained by Naimark [ 5 ] . Section 7. Most of the results given in this section are found in the literature only in the special case of operators of second order . Some of the theorems have ...
Page 1834
... second order linear differential equation . Duke Math . J. 17 , 57-62 ( 1950 ) . On self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33-47 ( 1952 ) . Sur la notion du groupe abstrait topologique . Fund ...
... second order linear differential equation . Duke Math . J. 17 , 57-62 ( 1950 ) . On self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33-47 ( 1952 ) . Sur la notion du groupe abstrait topologique . Fund ...
Page 1848
... second order . Doklady Akad . Nauk SSSR ( N.S. ) 85 , 41-44 ( 1952 ) . ( Russian ) Math . Rev. 14 , 473 ( 1953 ) . Investigation of the spectrum and expansion in eigenfunctions of singular non - self - adjoint differential operators of ...
... second order . Doklady Akad . Nauk SSSR ( N.S. ) 85 , 41-44 ( 1952 ) . ( Russian ) Math . Rev. 14 , 473 ( 1953 ) . Investigation of the spectrum and expansion in eigenfunctions of singular non - self - adjoint differential operators of ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 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 subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero