Linear Operators, Part 2 |
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Page 1792
... linear differential equations . Trans . Amer . Math . Soc . 9 , 373–395 ( 1908 ) . Existence and oscillation theorems for a certain boundary value problem . Trans . Amer . Math . Soc . 10 , 259-270 ( 1909 ) . Quantum mechanics and ...
... linear differential equations . Trans . Amer . Math . Soc . 9 , 373–395 ( 1908 ) . Existence and oscillation theorems for a certain boundary value problem . Trans . Amer . Math . Soc . 10 , 259-270 ( 1909 ) . Quantum mechanics and ...
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 1816
... equations in Hilbert spaces . Soobščeniya Akad . Nauk Gruzin . SSR 13 , 65–72 ( 1952 ) . ( Russian ) Math . Rev. 14 , 990 ( 1953 ) . On a class of linear equations with symmetrizable operators ... differential equations 1816 REFERENCES.
... equations in Hilbert spaces . Soobščeniya Akad . Nauk Gruzin . SSR 13 , 65–72 ( 1952 ) . ( Russian ) Math . Rev. 14 , 990 ( 1953 ) . On a class of linear equations with symmetrizable operators ... differential equations 1816 REFERENCES.
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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero