Linear Operators, Part 2 |
From inside the book
Results 1-3 of 92
Page 2025
... gives -n ( 40 ) 12 - − { x1 ( 8 ) | ′′ = n 1 = | 4 ( 8 ) | ≤ M n 1 , 2 , .... ( λ - w ) n - ω Since ( k ( s ) ) > w we may fix A so large that | λ — Яk , ( s ) ] < λ — w and thus the fraction appearing in ( 40 ) approaches zero as n ...
... gives -n ( 40 ) 12 - − { x1 ( 8 ) | ′′ = n 1 = | 4 ( 8 ) | ≤ M n 1 , 2 , .... ( λ - w ) n - ω Since ( k ( s ) ) > w we may fix A so large that | λ — Яk , ( s ) ] < λ — w and thus the fraction appearing in ( 40 ) approaches zero as n ...
Page 2031
... gives ( FT ) ( q ) = √ ( Fq ) ( 3 ) 4 ( 8 ) ds = | _ _p ( 8 ) ( F4 ) ( s ) ds = RN - > RN Un -- TFU ( 9 ) , ΦΕΦ Now is dense in H = L2 ( RN ) and thus there is for an arbitrary in 5 a sequence { n } with n → in 5. Since F ( XI.1 ) and ...
... gives ( FT ) ( q ) = √ ( Fq ) ( 3 ) 4 ( 8 ) ds = | _ _p ( 8 ) ( F4 ) ( s ) ds = RN - > RN Un -- TFU ( 9 ) , ΦΕΦ Now is dense in H = L2 ( RN ) and thus there is for an arbitrary in 5 a sequence { n } with n → in 5. Since F ( XI.1 ) and ...
Page 2065
... gives more by asserting that the inverse a - 1 is in A1 . The basic notions underlying the proof of Wiener's theorem as it will be presented here are those to be found in I. M. Gelfand's theory of com- mutative normed rings , or B ...
... gives more by asserting that the inverse a - 1 is in A1 . The basic notions underlying the proof of Wiener's theorem as it will be presented here are those to be found in I. M. Gelfand's theory of com- mutative normed rings , or B ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
26 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 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