2,763 research outputs found
Radiation diffusion in a medium with a strongly elongated scattering indicatrix
Approximation method for calculating radiation diffusion in medium with elongated scattering matri
On the Schatten-von Neumann properties of some pseudo-differential operators
We obtain a number of explicit estimates for quasi-norms of
pseudo-differential operators in the Schatten-von Neumann classes with
. The estimates are applied to derive semi-classical bounds for
operators with smooth or non-smooth symbols.Comment: 22 page
Planetary atmosphere albedo
Computation of plane and spherical albedo of planetary atmosphere
Wiener-Hopf operators in higher dimensions: the Widom conjecture for piece-wise smooth domains
We prove a two-term quasi-classical trace asymptotic formula for the
functions of multi-dimensional Wiener-Hopf operators with discontinuous
symbols. The discontinuities occur on the surfaces which are assumed to be
piece-wise smooth. Such a two-term formula was conjectured by H. Widom in 1982,
and proved by A. V Sobolev for smooth surfaces in 2009.Comment: 15 page
On a coefficient in trace formulas for Wiener-Hopf operators
Let be a smooth function quickly decreasing at
infinity. For the Wiener-Hopf operator with the symbol , and a smooth
function , H. Widom in 1982 established the following
trace formula: where is given explicitly in terms of
the functions and . The paper analyses the coefficient for a class of non-smooth functions assuming that is real-valued. A
representative example of one such function is with some
.Comment: 21 page
A family of anisotropic integral operators and behaviour of its maximal eigenvalue
We study the family of compact integral operators in
with the kernel K_\beta(x, y) = \frac{1}{\pi}\frac{1}{1 +
(x-y)^2 + \beta^2\Theta(x, y)}, depending on the parameter , where
is a symmetric non-negative homogeneous function of degree
. The main result is the following asymptotic formula for the
maximal eigenvalue of : M_\beta = 1 - \lambda_1
\beta^{\frac{2}{\gamma+1}} + o(\beta^{\frac{2}{\gamma+1}}), \beta\to 0, where
is the lowest eigenvalue of the operator . A central role in the proof is played by the fact that
is positivity improving. The case has been studied earlier in the literature as a simplified model
of high-temperature superconductivity.Comment: 16 page
- …