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 2545
... ( Russian ) Math . Rev. 15 , 720 ( 1954 ) . 22. Criteria for completeness of the system of root vectors of a dissipative operator . Uspehi Mat . Nauk 14 , no . 3 ( 87 ) , 145–152 ( 1959 ) . ( Russian ) Math . Rev. 22 # 9856 ( 1961 ) ...
... ( Russian ) Math . Rev. 15 , 720 ( 1954 ) . 22. Criteria for completeness of the system of root vectors of a dissipative operator . Uspehi Mat . Nauk 14 , no . 3 ( 87 ) , 145–152 ( 1959 ) . ( Russian ) Math . Rev. 22 # 9856 ( 1961 ) ...
Page 2549
... ( Russian ) Math . Rev. 33 # 4680 , 792 ( 1967 ) . 6. Expansion in characteristic functions of a non - selfadjoint differential operator with spectral singularities . Doklady Akad . Nauk SSSR 149 , 256-259 ( 1963 ) . ( Russian ) Soviet ...
... ( Russian ) Math . Rev. 33 # 4680 , 792 ( 1967 ) . 6. Expansion in characteristic functions of a non - selfadjoint differential operator with spectral singularities . Doklady Akad . Nauk SSSR 149 , 256-259 ( 1963 ) . ( Russian ) Soviet ...
Page 2552
... ( Russian ) Math . Rev. 27 # 1837 , 361 ( 1964 ) . 2. Eigenvalues and singular values of the sum and product of linear operators . Uspehi Mat . Nauk 19 , no . 4 ( 118 ) , 93–123 ( 1964 ) . ( Russian ) Math . Rev. 29 # 6318 , 1184 ( 1965 ) ...
... ( Russian ) Math . Rev. 27 # 1837 , 361 ( 1964 ) . 2. Eigenvalues and singular values of the sum and product of linear operators . Uspehi Mat . Nauk 19 , no . 4 ( 118 ) , 93–123 ( 1964 ) . ( Russian ) Math . Rev. 29 # 6318 , 1184 ( 1965 ) ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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