Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 86
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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
22 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero