Linear Operators: Spectral operators |
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Page 1176
Let p, q, k, be as in the preceding lemma, and, for each N, let 3% N be the
transformation in L,(l,) which maps the vector whose nth component has the
Fourier transform f,($) into the vector whose nth component has the Fourier
transform k,($)f ...
Let p, q, k, be as in the preceding lemma, and, for each N, let 3% N be the
transformation in L,(l,) which maps the vector whose nth component has the
Fourier transform f,($) into the vector whose nth component has the Fourier
transform k,($)f ...
Page 1751
o differentiable m-vector valued functions defined in C1. Similarly, C*(C1) and Co
(Cl) will denote the subspaces of C*(CI) consisting of all functions which are
multiply periodic of period 27 and of all functions which vanish outside a compact
...
o differentiable m-vector valued functions defined in C1. Similarly, C*(C1) and Co
(Cl) will denote the subspaces of C*(CI) consisting of all functions which are
multiply periodic of period 27 and of all functions which vanish outside a compact
...
Page 1786
Polon. Math. 19, 140–161 (1946), II. ibid. 19, 161–164 (1946). 3. On
differentiation of vector-valued functions. Studia Math. 11, 185-190 (1950). 4.
Continuity of vector-valued functions of bounded variation. Studia Math. 12, 133–
142 (1951). 5.
Polon. Math. 19, 140–161 (1946), II. ibid. 19, 161–164 (1946). 3. On
differentiation of vector-valued functions. Studia Math. 11, 185-190 (1950). 4.
Continuity of vector-valued functions of bounded variation. Studia Math. 12, 133–
142 (1951). 5.
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
4 Exercises | 879 |
Copyright | |
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Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 infinity integral interval kernel Lemma Let f Let Q 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 numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero