Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 1185
... applied to various problems in mathematical analysis . However , we have not as yet applied this theory to the important class of problems known as boundary value problems . This is because the operators arising in boundary value ...
... applied to various problems in mathematical analysis . However , we have not as yet applied this theory to the important class of problems known as boundary value problems . This is because the operators arising in boundary value ...
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 ...
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