312 research outputs found
Perturbation of spectra and spectral subspaces
We consider the problem of variation of spectral subspaces for linear
self-adjoint operators under off-diagonal perturbations. We prove a number of
new optimal results on the shift of the spectrum and obtain (sharp) estimates
on the norm of the difference of two spectral projections
On a Subspace Perturbation Problem
We discuss the problem of perturbation of spectral subspaces for linear
self-adjoint operators on a separable Hilbert space. Let and be bounded
self-adjoint operators. Assume that the spectrum of consists of two
disjoint parts and such that . We show that the norm of the difference of the spectral projections
\EE_A(\sigma) and \EE_{A+V}\big (\{\lambda | \dist(\lambda, \sigma)
for and is less then one whenever either (i)
or (ii) and certain assumptions on the
mutual disposition of the sets and are satisfied
Property control methods of diamond-like silicon-carbon films for micro- and nanoelectronics
Possible methods for controlling the properties of amorphous diamond-like silicon-carbon films are considered: physical or structural modification, chemical modification, and physical-chemical modification. It is shown that the method of physical modification allows controlling in a wide range the properties of diamondlike silicon-carbon films (electrophysical, mechanical properties and surface morphology) without changing the chemical composition of the material. Chemical modification was carried out by introducing transition metal into diamond-like silicon-carbon films. The dependences of the phase composition, electrophysical and mechanical properties on the content and type of metal are analyzed. The method of physical-chemical modification is considered, when the introduced impurity changes not only the chemical composition, but also the structure of the material
On the existence of solutions to the operator Riccati equation and the tan\Theta theorem
Let A and C be self-adjoint operators such that the spectrum of A lies in a
gap of the spectrum of C and let d>0 be the distance between the spectra of A
and C. We prove that under these assumptions the sharp value of the constant c
in the condition ||B||<cd guaranteeing the existence of a (bounded) solution to
the operator Riccati equation XA-CX+XBX=B^* is equal to \sqrt{2}. We also prove
an extension of the Davis-Kahan \tan\Theta theorem and provide a sharp estimate
for the norm of the solution to the Riccati equation. If C is bounded, we
prove, in addition, that the solution X is a strict contraction if B satisfies
the condition ||B||<d, and that this condition is sharp.Comment: Extended version of the pape
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