Linear Operators: Spectral operators |
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Page 1000
A similar argument shows that f,(z) → f, (3) uniformly on each compact subset on
the half-plane Z(z) > 0. If {fi} were known to be uniformly convergent in a
neighborhood of U, the analyticity of its limit fo would be clear. Unfortunately it is
not clear ...
A similar argument shows that f,(z) → f, (3) uniformly on each compact subset on
the half-plane Z(z) > 0. If {fi} were known to be uniformly convergent in a
neighborhood of U, the analyticity of its limit fo would be clear. Unfortunately it is
not clear ...
Page 1001
It is clear that f, converges uniformly on any portion of Q whose closure contains
neither a nor b. Let M be a bound for the sequence p, so that • M f,(a+ is) is Ms |e-
to le"dr = — , — 1 < s - 0. 0 |s| In the same way it is seen that |f,(a+is) < Ms- when
...
It is clear that f, converges uniformly on any portion of Q whose closure contains
neither a nor b. Let M be a bound for the sequence p, so that • M f,(a+ is) is Ms |e-
to le"dr = — , — 1 < s - 0. 0 |s| In the same way it is seen that |f,(a+is) < Ms- when
...
Page 1108
If 2,0m) is a parameter family of sequences such that (i) A, (m) → A, as m -- Co
uniformly in i, (ii) lim, ... X., |2,(m)}* = 0 uniformly in m, it follows that (iii) X., |2,(m)*
is bounded uniformly in m, (iv) A, (m) → 0 as i → CO uniformly in m. Thus, by the
...
If 2,0m) is a parameter family of sequences such that (i) A, (m) → A, as m -- Co
uniformly in i, (ii) lim, ... X., |2,(m)}* = 0 uniformly in m, it follows that (iii) X., |2,(m)*
is bounded uniformly in m, (iv) A, (m) → 0 as i → CO uniformly in m. Thus, by the
...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
4 Exercises | 879 |
Copyright | |
52 other sections not shown
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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