Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 92
Page 1989
... spectral measure in 5 , and thus , since F is unitary , the measure e ( σ ) , σ € Σ , is a spectral measure with these same properties . We also have e ( o ) = 0 if and only if o has Lebesgue measure zero so that the notions of e ...
... spectral measure in 5 , and thus , since F is unitary , the measure e ( σ ) , σ € Σ , is a spectral measure with these same properties . We also have e ( o ) = 0 if and only if o has Lebesgue measure zero so that the notions of e ...
Page 2107
... spectral ( respectively , scalar type ) operator , then T is spectral ( respectively , scalar type ) . A number of ... measure μ on X to A we mean a mapping 8 → μ ( S ) from the Baire field ( the o - field generated by the compact G ...
... spectral ( respectively , scalar type ) operator , then T is spectral ( respectively , scalar type ) . A number of ... measure μ on X to A we mean a mapping 8 → μ ( S ) from the Baire field ( the o - field generated by the compact G ...
Page 2110
... measure space and denote L2 μ ) . = L , ( S , E , μ ) . Let 1 ≤r≤8 ≤ + ∞ and let T be a spectral opera- tor on L , with resolution of the identity E. If T leaves L , invariant and T , TL , is spectral , then its resolution of the ...
... measure space and denote L2 μ ) . = L , ( S , E , μ ) . Let 1 ≤r≤8 ≤ + ∞ and let T be a spectral opera- tor on L , with resolution of the identity E. If T leaves L , invariant and T , TL , is spectral , then its resolution of the ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
36 other sections not shown
Other editions - View all
Common terms and phrases
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