Linear Operators, Part 2 |
From inside the book
Results 1-3 of 47
Page 2338
... finite number of the roots of M ( μ ) = 0 which lie in A1 are simple , and that they may be enumerated in a sequence έm in such a way that we have an asymptotic expression ( 49 ) 00 & m ~ 2πm ( 1+ Σ c2m- " ) . n = 1 The analysis of the ...
... finite number of the roots of M ( μ ) = 0 which lie in A1 are simple , and that they may be enumerated in a sequence έm in such a way that we have an asymptotic expression ( 49 ) 00 & m ~ 2πm ( 1+ Σ c2m- " ) . n = 1 The analysis of the ...
Page 2358
... finite number of indices i , the inequality ( ii ) gives us an immediate bound for the function f ( u ) = R ( μ ; T + P ) ƒ = B ( μ ) ƒ in all but a finite number of the sets V. By the maximum modulus principle this entire function has ...
... finite number of indices i , the inequality ( ii ) gives us an immediate bound for the function f ( u ) = R ( μ ; T + P ) ƒ = B ( μ ) ƒ in all but a finite number of the sets V. By the maximum modulus principle this entire function has ...
Page 2362
... finite number of the points in o ( 1 ' ) are simple poles of the resolvent function R ( λ ; T ) ; let { U1 } be a sequence of bounded domains covering the entire plane , such that lim , minge U1 | 2 | Ui = ∞ . It is assumed that the ...
... finite number of the points in o ( 1 ' ) are simple poles of the resolvent function R ( λ ; T ) ; let { U1 } be a sequence of bounded domains covering the entire plane , such that lim , minge U1 | 2 | Ui = ∞ . It is assumed that the ...
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