Linear Operators: Spectral operators |
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Page 1914
... kernel giving the solution to the Cauchy initial value problem of Theorem XV.12.19 and many other similar problems may be given as a finite expression involving only elementary functions . The explicit details of calculation are in the ...
... kernel giving the solution to the Cauchy initial value problem of Theorem XV.12.19 and many other similar problems may be given as a finite expression involving only elementary functions . The explicit details of calculation are in the ...
Page 2493
... kernels x ( x , y ) and B ( x , y ) . Then BR ( A ) A is the integral 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 ...
... kernels x ( x , y ) and B ( x , y ) . Then BR ( A ) A is the integral 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 ...
Page 2502
... kernel function & satisfies the integral inequality f | 8 ( X ) | d8 ≤ || H2 — H1 || 1 , 2 the norm on the right being the trace norm of Chapter XI . Moreover , Krein establishes the trace formula + ∞0 tr ( p ( H , ) –q ( H ) = [ 8 ) ...
... kernel function & satisfies the integral inequality f | 8 ( X ) | d8 ≤ || H2 — H1 || 1 , 2 the norm on the right being the trace norm of Chapter XI . Moreover , Krein establishes the trace formula + ∞0 tr ( p ( H , ) –q ( H ) = [ 8 ) ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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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