Linear Operators: Spectral theory |
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Page 1795
... Linear parabolic differential equations of arbitrary order ; general boundary- value problems for elliptic equations . Proc . Nat . Acad . Sci . U.S.A. 39 , 185-190 ( 1953 ) . Strongly elliptic systems of differential equations ...
... Linear parabolic differential equations of arbitrary order ; general boundary- value problems for elliptic equations . Proc . Nat . Acad . Sci . U.S.A. 39 , 185-190 ( 1953 ) . Strongly elliptic systems of differential equations ...
Page 1817
... differential equations . Amer . J. Math . 76 , 831-838 ( 1954 ) . Hartman , P. , and Putnam , C. 1. The least cluster point of the spectrum of boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the ...
... differential equations . Amer . J. Math . 76 , 831-838 ( 1954 ) . Hartman , P. , and Putnam , C. 1. The least cluster point of the spectrum of boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the ...
Page 1835
... differential equations of the second order . Gosudarstv . Izdat . Tehn . - Teor . Lit. , Moscow - Leningrad , 1950 . On a decomposition theorem for characteristic functions of differential equations of second order . Doklady Akad . Nauk ...
... differential equations of the second order . Gosudarstv . Izdat . Tehn . - Teor . Lit. , Moscow - Leningrad , 1950 . On a decomposition theorem for characteristic functions of differential equations of second order . Doklady Akad . Nauk ...
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