Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 75
Page 2325
... formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3.5 , formula ( 16 ) , and formula ( 14 ) , that the zero έn of M ( μ ) in RM ) has the asymptotic representation - ∞ §n ~ 2πn + a + z2 + Σ 5 m n − m = 1 -m " and that the zero ...
... formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3.5 , formula ( 16 ) , and formula ( 14 ) , that the zero έn of M ( μ ) in RM ) has the asymptotic representation - ∞ §n ~ 2πn + a + z2 + Σ 5 m n − m = 1 -m " and that the zero ...
Page 2330
... formula ( 26 ) that Em is given asymptotically by the formula ( 28 ) ( Emf ) ( t ) ~ n Σπί Co ~ iu { Ê Ans ( μ + 2mn ) e1 + Aks ( μ + 2πn ) e ̄1a + Aks ( μ + 2πn ) k.j = 1 iu kj A ( μ + 2πn ) e1μ + A ' ( μ + 2πn ) е − 1o + А ” ( μ + ...
... formula ( 26 ) that Em is given asymptotically by the formula ( 28 ) ( Emf ) ( t ) ~ n Σπί Co ~ iu { Ê Ans ( μ + 2mn ) e1 + Aks ( μ + 2πn ) e ̄1a + Aks ( μ + 2πn ) k.j = 1 iu kj A ( μ + 2πn ) e1μ + A ' ( μ + 2πn ) е − 1o + А ” ( μ + ...
Page 2340
... formula ( 42 ) . It now follows just as in Case 1A that the projection Em = E ( m ; T ) is given asymptotically by the formula n ( 57 ) ( Emf ) ( x ) ~ 2πί CO 0 1 n { Σ Aks ( μ2 + 2mm ) e1 + Aks ( μa + 2πm ) k , j = 1 А ( μ + 2πm ) e1μ ...
... formula ( 42 ) . It now follows just as in Case 1A that the projection Em = E ( m ; T ) is given asymptotically by the formula n ( 57 ) ( Emf ) ( x ) ~ 2πί CO 0 1 n { Σ Aks ( μ2 + 2mm ) e1 + Aks ( μa + 2πm ) k , j = 1 А ( μ + 2πm ) e1μ ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
35 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operators Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero