Linear Operators: Spectral operators |
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Page 1955
... spectrum of A is the set σ ( A ) of complex numbers À for which I — A is one - to - one and has a dense range which is not equal to X. The residual spectrum of A is the set σ ‚ ( A ) con- sisting of those complex numbers À for which IT ...
... spectrum of A is the set σ ( A ) of complex numbers À for which I — A is one - to - one and has a dense range which is not equal to X. The residual spectrum of A is the set σ ‚ ( A ) con- sisting of those complex numbers À for which IT ...
Page 2507
... spectrum of H , while the integrals and + ∞0 ƒ ̃ † ~ * ~ \ A ( ( \ ± ie ) I — H ̧ ) − 1v | 2 đλ + ∞ [ * | B ... spectrum of H can change drastically . In particular , the " absolutely continuous spectrum " o ( Hac ( h ) ) ( cf ...
... spectrum of H , while the integrals and + ∞0 ƒ ̃ † ~ * ~ \ A ( ( \ ± ie ) I — H ̧ ) − 1v | 2 đλ + ∞ [ * | B ... spectrum of H can change drastically . In particular , the " absolutely continuous spectrum " o ( Hac ( h ) ) ( cf ...
Page 2591
... Spectrum , of a spectral operator , XV.8 ( 1954 ) condition to be in point spectrum , XV.15.13 ( 2076 ) continuous spectrum , definition of , XV.8.1 ( 1955 ) examples of , XV.15.37 , XV.15.38 , XV.15.39 ( 2080 ) point spectrum ...
... Spectrum , of a spectral operator , XV.8 ( 1954 ) condition to be in point spectrum , XV.15.13 ( 2076 ) continuous spectrum , definition of , XV.8.1 ( 1955 ) examples of , XV.15.37 , XV.15.38 , XV.15.39 ( 2080 ) point spectrum ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 Borel function 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 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