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 2307
... order terms as pertur- bations . " In Section 4 below , we shall carry out this idea in detail . However , since the technical difficulties in the cases k > 2 are so annoying , we shall , in the next section , treat ... Second Order Operator.
... order terms as pertur- bations . " In Section 4 below , we shall carry out this idea in detail . However , since the technical difficulties in the cases k > 2 are so annoying , we shall , in the next section , treat ... Second Order Operator.
Page 2397
... such that ( 41 ) ƒ® ̊ | C ( ƒ , 9 , λ ) | dλ ≤ K | ƒ | 2 | 9 \ 2 , f , ge Co [ 0 , ∞ ) . Put ( 42 ) ( Ø * ƒ ) ( XX.1.12 SPECTRAL DIFFERENTIAL OPERAtors of secOND ORDER 2397 Spectral Differential Operators of Second Order.
... such that ( 41 ) ƒ® ̊ | C ( ƒ , 9 , λ ) | dλ ≤ K | ƒ | 2 | 9 \ 2 , f , ge Co [ 0 , ∞ ) . Put ( 42 ) ( Ø * ƒ ) ( XX.1.12 SPECTRAL DIFFERENTIAL OPERAtors of secOND ORDER 2397 Spectral Differential Operators of Second Order.
Page 2556
... second order . Doklady Akad . Nauk SSSR ( N. S. ) 89 , 213–216 ( 1953 ) . ( Russian ) Math . Rev. 15 , 33 ( 1954 ) . 12. Investigation of the spectrum and the expansion in eigenfunctions of a non : self - adjoint operator of the second ...
... second order . Doklady Akad . Nauk SSSR ( N. S. ) 89 , 213–216 ( 1953 ) . ( Russian ) Math . Rev. 15 , 33 ( 1954 ) . 12. Investigation of the spectrum and the expansion in eigenfunctions of a non : self - adjoint operator of the second ...
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