Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 42
Page 2394
... independent , we must have a linear relation σ2 = aô1 + bơ1 . It is clear from Lemma 1 that such a linear combination can only have the indicated asymptotic form if a = 1 , b = c ( μ ( λ ) ) . Hence σ2 ( t , μ ( \ ) ) = σ1 ( t , −μ ( λ ) ...
... independent , we must have a linear relation σ2 = aô1 + bơ1 . It is clear from Lemma 1 that such a linear combination can only have the indicated asymptotic form if a = 1 , b = c ( μ ( λ ) ) . Hence σ2 ( t , μ ( \ ) ) = σ1 ( t , −μ ( λ ) ...
Page 2425
... independent of y , B and ƒ such that ( 37 ) + ∞ 1/2 ds + ∞ 1/2 { { { * _ * _ \ 9 ( 0 ) 2 da } * ≤ N { { ** [ S ( 9 ) P2 de ) ** . -∞ ds This we do as follows . Let { x , a E A } be a complete orthonormal basis for H. Then ( 38 ) ( 9 ...
... independent of y , B and ƒ such that ( 37 ) + ∞ 1/2 ds + ∞ 1/2 { { { * _ * _ \ 9 ( 0 ) 2 da } * ≤ N { { ** [ S ( 9 ) P2 de ) ** . -∞ ds This we do as follows . Let { x , a E A } be a complete orthonormal basis for H. Then ( 38 ) ( 9 ...
Page 2441
... independent of ɛ such that 4 4 ( 43 ) [ V1 ( r , r ' ) | + | OV / s ( r , r ' ) | + | os r av av ( r , r ' ) Ər ( r , r ' ) 1 | + | 27 ( n ) | + | 27 ( n ) | ar ' Ər Ər ' ≤M " ε ( 1 + max ( r , r ' ) ) − n + 1 ̧ Put V5 ( r , r ' ) = ...
... independent of ɛ such that 4 4 ( 43 ) [ V1 ( r , r ' ) | + | OV / s ( r , r ' ) | + | os r av av ( r , r ' ) Ər ( r , r ' ) 1 | + | 27 ( n ) | + | 27 ( n ) | ar ' Ər Ər ' ≤M " ε ( 1 + max ( r , r ' ) ) − n + 1 ̧ Put V5 ( r , r ' ) = ...
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