Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 77
Page 1933
... resolvent of a bounded spectral operator have a number of important properties not enjoyed by functions of the form R ( ; T ) x when T is not a spectral operator . In ... RESOLVENT OF A SPECTRAL OPERATOR The Resolvent of a Spectral Operator.
... resolvent of a bounded spectral operator have a number of important properties not enjoyed by functions of the form R ( ; T ) x when T is not a spectral operator . In ... RESOLVENT OF A SPECTRAL OPERATOR The Resolvent of a Spectral Operator.
Page 2291
... resolvent occurs so frequently in this section , it will be convenient to introduce , in the following definition , a special term for such operators . 1 DEFINITION . An operator T is discrete if there is a number à in its resolvent set ...
... resolvent occurs so frequently in this section , it will be convenient to introduce , in the following definition , a special term for such operators . 1 DEFINITION . An operator T is discrete if there is a number à in its resolvent set ...
Page 2316
... resolvent . By Lemma 8 , the condition for this is ( pn , n ) = 0 , where is a solution of ( T * — Xn I * ) $ n = 0 . n Since by Theorems XIII.2.10 and XII.4.28 , T * is defined by the formal differential operator ( d / dt ) 2 and the ...
... resolvent . By Lemma 8 , the condition for this is ( pn , n ) = 0 , where is a solution of ( T * — Xn I * ) $ n = 0 . n Since by Theorems XIII.2.10 and XII.4.28 , T * is defined by the formal differential operator ( d / dt ) 2 and the ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
22 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero