Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 13
Page 2450
... operator I + T ( A ) has a bounded inverse . We have now shown that equation ... operator . By Theorem X.3.4 there exists a complete orthonormal basis { x } ... Hilbert- Schmidt class HS , and let ||| A |||| || RA || , so that the norm ...
... operator I + T ( A ) has a bounded inverse . We have now shown that equation ... operator . By Theorem X.3.4 there exists a complete orthonormal basis { x } ... Hilbert- Schmidt class HS , and let ||| A |||| || RA || , so that the norm ...
Page 2489
... operators A , B of Hilbert - Schmidt class depending only on V and μ such that if we Zac ( H1 ) and w1 < ∞ then H1 | ( W + − U ̧ ) w | 2 ≤ ( § ̧a® \ 4 exp ( −ixH1 ) w | 2 dx − S 1/2 1/2 X ( [ ̧ TM | B exp ( −ixH1 ) w | 2 dx S ...
... operators A , B of Hilbert - Schmidt class depending only on V and μ such that if we Zac ( H1 ) and w1 < ∞ then H1 | ( W + − U ̧ ) w | 2 ≤ ( § ̧a® \ 4 exp ( −ixH1 ) w | 2 dx − S 1/2 1/2 X ( [ ̧ TM | B exp ( −ixH1 ) w | 2 dx S ...
Page 2493
... operator with the kernel pb b ( x , t ) a ( t , y ) · dt ; this kernel is Hölder - continuous in all the three parameters λ , x , y . If we let ( A ) = det ( I - BR ( A ) A ) be the Hilbert - Fredholm determi- nant of the Hilbert - Schmidt ...
... operator with the kernel pb b ( x , t ) a ( t , y ) · dt ; this kernel is Hölder - continuous in all the three parameters λ , x , y . If we let ( A ) = det ( I - BR ( A ) A ) be the Hilbert - Fredholm determi- nant of the Hilbert - Schmidt ...
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