Related papers: Space quasiconformal composition operators with ap…

In this paper we study the rate of convergence of the eigenvalues of 1-dimensional rapidly oscillating $p-$laplacian type problems and find explicit order of convergence both in $k$ and in $\ve$. Moreover, explicit bounds on the constant…

In this paper we study eigenvalues of Laplacian and biharmonic operators on compact domains in complete manifolds. We establish several new inequalities for eigenvalues of Laplacian and biharmonic operators respectively by using Sobolev…

We introduce new classes of modulation spaces over phase space. By means of the Kohn-Nirenberg correspondence, these spaces induce norms on pseudo-differential operators that bound their operator norms on $L^p$-spaces, Sobolev spaces, and…

We establish inequalities for the eigenvalues of Schr\"{o}dinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, complex and quaternionic projective spaces, which are related…

The article is devoted to the study of mappings that satisfy the so-called inverse Poletsky inequality. We consider mappings of quasiextremal distance domains, domains with a locally quasiconformal boundary, and domains which are regular in…

We obtain upper bounds for the eigenvalues of the Schr\"odinger operator $L=\Delta_g+q$ depending on integral quantities of the potential $q$ and a conformal invariant called the min-conformal volume. Moreover, when the Schr\"odinger…

Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and…

This paper considers composition operators on Zen spaces (a class of weighted Bergman spaces of the right half-plane related to weighted function spaces on the positive half-line by means of the Laplace transform). Generalizations are given…

In this work we analyze convergence of solutions for the Laplace operator with Neumann boundary conditions in a two-dimensional highly oscillating domain which degenerates into a segment (thin domains) of the real line. We consider the case…

Given a Schr\"odinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann and Dirichlet boundary conditions, respectively. The…

This is an update on the quasicentral modulus, an invariant for an n-tuple of Hilbert space operators and a rearrangement invariant norm, that plays a key-role in sharp multivariable generalizations of the classical Weyl-von Neumann-Kuroda…

On a smooth, compact, $n$-dimensional Riemannian manifold, we consider functions $u_h$ that are joint quasimodes of two semiclassical pseudodifferential operators $p_1(x,hD)$ and $p_2(x,hD)$. We develop $L^p$ estimates for $u_h$ when the…

We study various properties of quasimodular forms by using their connections with Jacobi-like forms and pseudodifferential operators. Such connections are made by identifying quasimodular forms for a discrete subgroup $\G$ of $SL(2, \bR)$…

We design quasi-interpolation operators based on piecewise polynomial weight functions of degree less than or equal to $p$ that map into the space of continuous piecewise polynomials of degree less than or equal to $p+1$. We show that the…

We establish the $L^p$ restriction estimates for quasimodes on a smooth curve in two dimensions. Our estimates are sharp for all smooth curves. As an application, we address $L^p$ eigenfunction restriction estimates for Laplace-Beltrami…

For $1\leq q \leq n-2$, we provide explicit examples to demonstrate non-compactness of the Neumann operator for the Kohn Laplacian acting on $L^2$ $(0,q)$-forms on the unit ball in $(2n+1)$-dimensional Heisenberg space.

In this paper we study geometric aspects of Ball's classes in the context of nonlinear elasticity problems. The suggested approach is based on the characterization of Ball's classes $A_{q,q'}(\Omega)$ in terms of composition operators on…

The p-Laplace operator in the entire N-dimensional Euclidean space, subject to external electromagnetic potentials, is investigated. In the general case 1<p<N, the existence of at least one solution of mountain pass type to a weighted…

In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in $N-$dimensional domains $\Omega$. We also consider singular and degenerate elliptic problems with $A_p$ coefficients involving the…

Given a quasiconformal mapping $f:\mathbb R^n\to\mathbb R^n$ with $n\ge2$, we show that (un-)boundedness of the composition operator ${\bf C}_f$ on the spaces $Q_{\alpha}(\mathbb R^n)$ depends on the index $\alpha$ and the degeneracy set of…