Linear Operators: Spectral operators |
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Page 1902
... section is dependent on any section to which it is connected by a rising line , except that ( b ) a section dependent on a dotted section , or on a section in Volume I or Volume II ( Chapters I - XIV ) , is dependent on every section on ...
... section is dependent on any section to which it is connected by a rising line , except that ( b ) a section dependent on a dotted section , or on a section in Volume I or Volume II ( Chapters I - XIV ) , is dependent on every section on ...
Page 2102
... Section 7 relating properties of a spectral operator and its scalar part are due to Foguel [ 2 ] , as are most of the results in Section 8 concerning the spectral properties of T , S , and N. Oberai [ 2 ] discussed some of these results ...
... Section 7 relating properties of a spectral operator and its scalar part are due to Foguel [ 2 ] , as are most of the results in Section 8 concerning the spectral properties of T , S , and N. Oberai [ 2 ] discussed some of these results ...
Page 2291
... Section 3 is greatly generalized in Section 4 , we feel that it is worth inserting the simpler case of Section 3 as a kind of preparation for the more complicated case . The question of deciding when the generalized eigenfunctions of an ...
... Section 3 is greatly generalized in Section 4 , we feel that it is worth inserting the simpler case of Section 3 as a kind of preparation for the more complicated case . The question of deciding when the generalized eigenfunctions of an ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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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