Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 1912
... Fourier transform , thus avoiding any reference to Section XI.3 where this theory is developed for locally compact groups by using the general spectral theorem which involves a more complex treatment than that found in Section XV.11 ...
... Fourier transform , thus avoiding any reference to Section XI.3 where this theory is developed for locally compact groups by using the general spectral theorem which involves a more complex treatment than that found in Section XV.11 ...
Page 1985
... Fourier and is contained in the following theorem . → 1 THEOREM . The Fourier transform is a homeomorphic isomorphism of onto all of itself whose inverse is ( 5 ) 1 9 ( 8 ) = [ ___elst ( Fq ) ( t ) dt , ( 2π ) N / 2 RN SERN PROOF ...
... Fourier and is contained in the following theorem . → 1 THEOREM . The Fourier transform is a homeomorphic isomorphism of onto all of itself whose inverse is ( 5 ) 1 9 ( 8 ) = [ ___elst ( Fq ) ( t ) dt , ( 2π ) N / 2 RN SERN PROOF ...
Page 2174
... Fourier - Stieltjes transform of its resolution E of the identity ; hence E can be considered to be the inverse Fourier - Stieltjes transform of the group { e - 21t | te R } . Assuming that this group is bounded in B ( X ) where X is ...
... Fourier - Stieltjes transform of its resolution E of the identity ; hence E can be considered to be the inverse Fourier - Stieltjes transform of the group { e - 21t | te R } . Assuming that this group is bounded in B ( X ) where X is ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero