Linear Operators, Part 2 |
From inside the book
Results 1-3 of 72
Page 2029
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) ዋ T1 ( q ) = √__p ( s ) v ( ds ) , RN ΦΕΦ Similarly , functions on RN may determine ...
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) ዋ T1 ( q ) = √__p ( s ) v ( ds ) , RN ΦΕΦ Similarly , functions on RN may determine ...
Page 2054
... determined continuous map t → q ( t ) of [ 0 , ∞ ) into H2 ( of ( —∞0 , 0 ] into H2 if a2 < 0 ) which is differentiable for t > 0 and has the properties ( iii ) ( iv ) ( v ) p ( t ) e ( 2 ) T ( 2 ) ( RN ) , t > 0 . q ' ( t ) = A ̧ p ...
... determined continuous map t → q ( t ) of [ 0 , ∞ ) into H2 ( of ( —∞0 , 0 ] into H2 if a2 < 0 ) which is differentiable for t > 0 and has the properties ( iii ) ( iv ) ( v ) p ( t ) e ( 2 ) T ( 2 ) ( RN ) , t > 0 . q ' ( t ) = A ̧ p ...
Page 2373
... determine discrete differential operators having eigenvalues = s2 determined by equations of the form sin s = ks . In this case the eigenvalues are located asymptotically at the points an2 + ibn In n + ... , the ratio of a and b being ...
... determine discrete differential operators having eigenvalues = s2 determined by equations of the form sin s = ks . In this case the eigenvalues are located asymptotically at the points an2 + ibn In n + ... , the ratio of a and b being ...
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