Linear Operators, Part 2 |
From inside the book
Results 1-3 of 66
Page 1930
... domain contains at most a finite number of disjoint sets . Thus we are led to the following definition and corollary ... domain of E. COROLLARY . If the domain of a countably additive spectral 1930 XV.2.2 XV . SPECTRAL OPERATORS.
... domain contains at most a finite number of disjoint sets . Thus we are led to the following definition and corollary ... domain of E. COROLLARY . If the domain of a countably additive spectral 1930 XV.2.2 XV . SPECTRAL OPERATORS.
Page 2087
... domain ( p ) T ( 24 ) ( RN ) is the infinitesimal generator of a strongly continuous semi - group S ( t ) , t≥ 0 ... domain D ( D ) of the natural closed extension of D contains ( p ) T ( 24 ) ( RN ) and the operator Ag + D + B with ...
... domain ( p ) T ( 24 ) ( RN ) is the infinitesimal generator of a strongly continuous semi - group S ( t ) , t≥ 0 ... domain D ( D ) of the natural closed extension of D contains ( p ) T ( 24 ) ( RN ) and the operator Ag + D + B with ...
Page 2256
... domain D1 containing the union of o ( T ) and a neighborhood of infinity , C1 being oriented in the customary positive sense of complex variable theory . The curves C of the present lemma bound a finite domain D containing every point ...
... domain D1 containing the union of o ( T ) and a neighborhood of infinity , C1 being oriented in the customary positive sense of complex variable theory . The curves C of the present lemma bound a finite domain D containing every point ...
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