Linear Operators: Spectral theory |
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Page 849
... Differential and Integral Equations By K. Yosida Representation Theory of Finite Groups and Associative Algebras By C. W. Curtis and I. Reiner Additional volumes in preparation PURE AND APPLIED MATHEMATICS A Series of Texts and Monographs.
... Differential and Integral Equations By K. Yosida Representation Theory of Finite Groups and Associative Algebras By C. W. Curtis and I. Reiner Additional volumes in preparation PURE AND APPLIED MATHEMATICS A Series of Texts and Monographs.
Page 1278
... applied " to a function f , if , say , f belongs to C " . Thus , we can define an operator whose domain is C " ( but whose range is not in C " , only in C ) . We might , however , have “ applied " the formal differential operator to a ...
... applied " to a function f , if , say , f belongs to C " . Thus , we can define an operator whose domain is C " ( but whose range is not in C " , only in C ) . We might , however , have “ applied " the formal differential operator to a ...
Page 1584
... applied . To Hilb we also owe the first remark on the fundamental dichotomy arising in the bound- ary value theory of a second order differential operator with real coefficients , exhibited by the definite or indefinite character of the ...
... applied . To Hilb we also owe the first remark on the fundamental dichotomy arising in the bound- ary value theory of a second order differential operator with real coefficients , exhibited by the definite or indefinite character of the ...
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