Related papers: Relative Morse index theory and applications in wa…
We recall a Moure theory adapted to non self-adjoint operators and we apply this theory to Schr{\"o}dinger operators with non real potentials, using different type of conjugate operators. We show that some conjugate operators permits to…
The notion of index for arbitrary real factors is introduced and investigated. The main tool in our approach is the reduction of real factors to involutive *-anti-automorphisms of their complex enveloping von Neumann algebras. Similar to…
We provide a probabilistic characterization of criticality, subcriticality, and supercriticality for subordinated Schr\"{o}dinger operators. We also investigate the relationship between the subcriticality of these operators and the uniform…
In this paper, we study semilinear elliptic equations in domains where there is a natural class of solutions, which depend only on one variable, and whose simple geometry reflects the geometry of the domain. We prove that under quite…
The classical theory of attractive central force problem on the standard (flat) Euclidean plane can be generalized to surfaces by reformulating the basic underlying physical principles by means of differential geometry. Attractive central…
We study analytically and numerically the existence and orbital stability of the peak-standing-wave solutions for the cubic-quintic nonlinear Schrodinger equation with a point interaction determined by the delta of Dirac. We study the cases…
Using the theory of fixed point index, we establish new results for the existence of nonzero solutions of Hammerstein integral equations with reflections. We apply our results to a first order periodic boundary value problem with…
On complex algebraic varieties, height functions arising in combinatorial applications fail to be proper. This complicates the description and computation via Morse theory of key topological invariants. Here we establish checkable…
The paper is a presentation of recent investigations on potential scattering in R^3. We advocate a new formula for the wave operators and deduce the various outcomes that follow from this formula. A topological version of Levinson's theorem…
In this note Levinson theorems for Schroedinger operators in R^n with one point interaction at 0 are derived using the concept of winding numbers. These results are based on new expressions for the associated wave operators.
We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the…
We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications…
In this paper we prove a relative index theorem for pairs of generalized Dirac operators on orbifolds which are the same at infinity. This generalizes to orbifolds a celebrated theorem of Gromov and Lawson.
A family of discrete Schroedinger operators is investigated through scattering theory. The continuous spectrum of these operators exhibit changes of multiplicity, and some of these operators possess resonances at thresholds. It is shown…
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…
We show how some Hamiltonians may be approximated using rotating wave approximation methods. In order to achieve this we use the algebra of boson ladder operators, and transformation formulas between normal and symmetric ordering of the…
We prove the upper-semi-continuity of the Morse index plus nullity of critical points to general conformally invariant Lagrangians in dimension 2 under weak convergence. Precisely we establish that the sum of the Morse indices and the…
In the context of discrete Morse theory, we introduce Morse frames, which are maps that associate a set of critical simplexes to all simplexes. The main example of Morse frames are the Morse references. In particular, these Morse references…
We present improved approximation bounds for the Moore-Penrose inverses of banded matrices, where the bandedness is induced by a metric on the index set. We show that the pseudoinverse of a banded matrix can be approximated by another…
Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some C*-algebras of pseudo-differential operators with coefficients which either have…