Spectral asymptotics of Kreĭn–Feller operators for weak Gibbs measures on self-conformal fractals with overlaps

Spectral Asymptotics of Laplace Operators on Surfaces with Cusps

Hausdorff Dimension of Random Fractals with Overlaps

The term fractal was first introduced by Mandelbrot to denote sets with highly irregular structures. Mandelbrot and others have then used fractals to model various natural phenomena (for example, [19, 2]). A mathematical development of fractals via the theory of (non-random) self-similar sets and measures was given by Hutchinson [12]. A family of contractive maps {Sj}^ on E m is called an itera...

Multivariable Spectral Multipliers and Analysis of Quasielliptic Operators on Fractals

We study multivariable spectral multipliers F (L1, L2) acting on Cartesian product of ambient spaces of two self-adjoint operators L1 and L2. We prove that if F satisfies Hörmander type differentiability condition then the operator F (L1, L2) is of Calderón-Zygmund type. We apply obtained results to the analysis of quasielliptic operators acting on product of some fractal spaces. The existence ...

Spectral Asymptotics for Schrödinger Operators with Periodic Point Interactions

Spectrum of the second-order differential operator with periodic point interactions in L2 R is investigated. Classes of unitary equivalent operators of this type are described. Spectral asymptotics for the whole family of periodic operators are calculated. It is proven that the first several terms in the asymptotics determine the class of equivalent operators uniquely. It is proven that the spe...

Spectral Asymptotics for Dirichlet Elliptic Operators with Non-smooth Coefficients

We consider a 2m-th-order elliptic operator of divergence form in a domain  of Rn, assuming that the coefficients are Hölder continuous of exponent r 2 (0, 1]. For the self-adjoint operator associated with the Dirichlet boundary condition we improve the asymptotic formula of the spectral function e( 2m , x , y) for x = y to obtain the remainder estimate O( n + dist(x , ) 1 n 1) with any 2 (0,...