We consider a version of the Weyl formula describing the asymptotic behaviour of the counting function of eigenvalues in the semiclassical approximation for self-adjoint elliptic differential operators under weak regularity hypotheses. Our aim is to treat Hölder continuous coefficients and to investigate the case of critical energy values as well.

An eigenvalue criterion for hypercyclicity due to the first author is improved. As a consequence, some new sufficient conditions for a sequence of infinite order linear differential operators to be hypercyclic on the space of holomorphic functions on certain domains of ${ℂ}^N$ are shown. Moreover, several necessary conditions are furnished. The equicontinuity of a family of operators as above is also studied, and it is characterized if the domain is ${ℂ}^N$. The results obtained extend or improve earlier work...

We extend the results in [5] to non-compactly supported perturbations for a class of symmetric first order systems.

In the context of the spaces of homogeneous type, given a family of operators that look like approximations of the identity, new sharp maximal functions are considered. We prove a good-λ inequality for Muckenhoupt weights, which leads to an analog of the Fefferman-Stein estimate for the classical sharp maximal function. As a consequence, we establish weighted norm estimates for certain singular integrals, defined on irregular domains, with Hörmander conditions replaced by some estimates which do...

We describe the asymptotic distribution of eigenvalues of self-adjoint elliptic differential operators, assuming that the first-order derivatives of the coefficients are Lipschitz continuous. We consider the asymptotic formula of Hörmander's type for the spectral function of pseudodifferential operators obtained via a regularization procedure of non-smooth coefficients.

We consider an abstract non-negative self-adjoint operator L acting on L²(X) which satisfies Davies-Gaffney estimates. Let $H_L^p\left(X\right)$ (p > 0) be the Hardy spaces associated to the operator L. We assume that the doubling condition holds for the metric measure space X. We show that a sharp Hörmander-type spectral multiplier theorem on $H_L^p\left(X\right)$ follows from restriction-type estimates and Davies-Gaffney estimates. We also establish a sharp result for the boundedness of Bochner-Riesz means on $H_L^p\left(X\right)$.

Let $M$ be a Riemannian manifold, which possesses a transitive Lie group $G$ of isometries. We suppose that $G$, and therefore $M$, are compact and connected. We characterize the Sobolev spaces $W_p^1\left(M\right)$$ 1 < p <... Solution of a spectral problem for the curl and the Stokes operator with periodic boundary conditions. Saks, R.S. (2004) Zapiski Nauchnykh Seminarov POMI Solution of a spectral problem for the curl operator on a cylinder. Saks, Romen, Vanegas, Carmen Judith (2005) Electronic Journal of Differential Equations (EJDE) [electronic only] Solutions analytiques et hyperfonctions du problème de Cauchy pour les opérateurs hyperboliques non stricts J. M. Bony, P. Schapira (1971/1972) Séminaire Équations aux dérivées partielles (Polytechnique) Solvability conditions for elliptic problems with non-Fredholm operators V. Volpert, B. Kaźmierczak, M. Massot, Z. Peradzyński (2002) Applicationes Mathematicae The paper is devoted to solvability conditions for linear elliptic problems with non-Fredholm operators. We show that the operator becomes normally solvable with a finite-dimensional kernel on properly chosen subspaces. In the particular case of a scalar equation we obtain necessary and sufficient solvability conditions. These results are used to apply the implicit function theorem for a nonlinear elliptic problem; we demonstrate the persistence of travelling wave solutions to spatially periodic... Solvability of linear and semilinear eigenvalue problems with L 1 data Luigi Orsina (1993) Rendiconti del Seminario Matematico della Università di Padova Some estimates of Schrödinger-type operators with certain nonnegative potentials. Liu, Yu, Ding, Youzheng (2008) International Journal of Mathematics and Mathematical Sciences Some generic properties of nonlinear second order diffusional type problem Vladimír Ďurikovič, Mária Ďurikovičová (1999) Archivum Mathematicum We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij’s decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem. Currently displaying 321 – 340 of 502 Previous Page 17 Next $