Related papers: Spectral estimates for degenerate critical levels
We derive a priori interior Hessian estimates for special Lagrangian equation with critical and supercritical phases in general higher dimensions. Our unified approach leads to sharper estimates even for the previously known three…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
In perturbation theory, the spectral densities of two-point functions develop non-integrable threshold singularities at higher orders. In QCD, such singularities emerge when calculating the diagrams in terms of the pole quark mass, and they…
We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…
In this work a spectral theory for 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation is developed. Spectral data for such solutions are defined (following Hitchin and Bobenko) and the space of spectral…
For the complex Ginibre ensemble subjected to an additive perturbation by a deterministic normal matrix $X_0$, we establish that under specific spectral conditions on $X_0$, only two distinct types of local spectral statistics emerge at the…
The Gram spectrahedron $\text{Gram}(f)$ of a form $f$ with real coefficients parametrizes the sum of squares decompositions of $f$, modulo orthogonal equivalence. For $f$ a sufficiently general positive binary form of arbitrary degree, we…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
A lighting-based multispectral imaging system using an RGB camera and a projector is one of the most practical and low-cost systems to acquire multispectral observations for estimating the scene's spectral reflectance information. However,…
A new approach to provide a fruitful analysis of signal amplitude is proposed. It is this method that has made it possible to eliminate some observed artificial events from the list of candidates for decays of superheavy nuclei. Examples of…
We derive a discrete spectral representation of the single-particle self-energy using a discrete evaluation of Kugler's symmetric improved estimator. Our construction can be used on both the real and the complex (Matsubara) frequency axis.…
We present a calculation of nuclear matter which goes beyond the usual quasi-particle approximation in that it includes part of the off-shell dependence of the self-energy in the self-consistent solution of the single-particle spectrum. The…
In this paper we prove that a class of non self-adjoint second order differential operators acting in cylinders $\Omega\times\mathbb R\subseteq\mathbb R^{d+1}$ have only real discrete spectrum located to the right of the right most point of…
Under various conditions, we establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H\"older semi-norms not with respect to all, but only with respect to some of the…
We generalize $\epsilon$-pseudospectra and the associated computational algorithms to the generalized eigenvalue problem. Rank one perturbations are used to determine the $\epsilon$-pseudospectra.
H\"older estimates and Harnack inequalities are studied for fully nonlinear integro-differential equations under some mild assumptions. We allow the kernels of variable order and critically close to 2.
In solar physics, especially in exploratory stages of research, it is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might…
We study asymptotics of fiber integrals depending on a large parameter. When the critical fiber is singular, full-asymptotic expansions are established in two different cases : local extremum and isolated real principal type singularities.…
The scope of this work is to propose a method for testing the integrability of a model partial differential (PDE) and/or differential difference equation (DDE). For monoparametric families of PDE/DDE's, that are known to possess isolated…
The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out…