Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 42
Page 2307
... formal differential operators and sets of boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple form ( d / dt ) and then to use Theorem ...
... formal differential operators and sets of boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple form ( d / dt ) and then to use Theorem ...
Page 2318
... function and T be the unbounded differential operator defined by a formal differential operator T = - d \ 2 dx + q ( x ) and by the boundary conditions [ * ] . Then T is a spectral operator . PROOF . This follows immediately from ...
... function and T be the unbounded differential operator defined by a formal differential operator T = - d \ 2 dx + q ( x ) and by the boundary conditions [ * ] . Then T is a spectral operator . PROOF . This follows immediately from ...
Page 2371
... differential equations , and by C. E. Wilder [ 1 , 2 ] , who studied the case in which linear conditions are imposed at interior points of the interval of definition of a formal differential operator . The abstract operator - theoretic ...
... differential equations , and by C. E. Wilder [ 1 , 2 ] , who studied the case in which linear conditions are imposed at interior points of the interval of definition of a formal differential operator . The abstract operator - theoretic ...
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