Related papers: A perturbation approach for Paneitz energy on stan…
We study a concentration problem on the unit sphere $\mathbb{S}^2$ for band-limited spherical harmonics expansions using large sieve methods. We derive upper bounds for concentration in terms of the maximum Nyquist density. Our proof uses…
In this work we consider, in a Banach space framework, the regularization of linear ill-posed problems. Our focus is on the recovery of solutions that have a logarithmic source representation. Such cases typically occur in exponentially…
Recently, Steinerberger proved a uniform inequality for the Laplacian serving as a counterpoint to the standard uniform sublevel set inequality which is known to fail for the Laplacian. In this note, we give an elementary proof of this…
Using an infinitesimal approach, this work addresses the renormalization problem to deal with the ultraviolet divergences arising in quantum field theory. Under the assumption that the action has already been renormalized to yield an…
A new general approach is introduced for definining an optimum zero-order Hamiltonian for Rayleigh-Schr\"odinger perturbation theory. Instead of taking the operator directly from a model problem, it is constructed to be a best fit to the…
We prove a comparison theorem for the averages of the solutions of two exterior parabolic problems, the second being the "symmetrization" of the first one, by using approximation of the Schwarz symmetrization by polarizations, as it was…
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…
We show several variants of concentration inequalities on the sphere stated as subgaussian estimates with optimal constants. For a Lipschitz function, we give one-sided and two-sided bounds for deviation from the median as well as from the…
We give a simple proof of a pointwise decay estimate in 3+1 dimensions stated in two versions, making advantage of a particular simplicity of inverting the spherically symmetric part of the wave operator and of the comparison theorem. We…
A new gridding technique for the solution of partial differential equations in cubical geometry is presented. The method is based on volume penalization, allowing for the imposition of a cubical geometry inside of its circumscribing sphere.…
We study perturbation theory in certain quantum mechanics problems in which the perturbing potential diverges at some points, even though the energy eigenvalues are smooth functions of the coefficient of the potential. We discuss some of…
This paper deals with homogenization of parabolic problems for integral convolution type operators with a non-symmetric jump kernel in a periodic elliptic medium. It is shown that the homogenization result holds in moving coordinates. We…
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case.…
The perturbation method is applied to numerical solution of the Lane-Emden Equation of arbitrary index n, and the global parameters of polytropes are found as function of polytropic index n.
This paper determines the sharp asymptotic order of the following reverse H\"older inequality for spherical harmonics $Y_n$ of degree $n$ on the unit sphere $\mathbb{S}^{d-1}$ of $\mathbb{R}^d$ as $n\to \infty$:…
High-temperature resummed perturbation theory is plagued by poor convergence properties. The problem appears for theories with bosonic field content such as QCD, QED or scalar theories. We calculate the pressure as well as other…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
We consider discontinuous perturbations of smooth endomorphisms and show that if the perturbed family satisfies uniform mixing assumptions on standard pairs the physical measure is Lipschitz in the parameter defying the perturbation. We…
In this article, we consider the linear operator equation in a Banach space. The relative perturbation of the solution x corresponding to the perturbation of y, the perturbation of A and the perturbation of both A, y are characterized from…
In this paper both we establish the best constants for the Nash inequalities on the standard unit sphere $\mathbb{S}^n$ of $\mathbb{R}^{n+1}$ and we give answers on the existence of extremal functions on the corresponding problems. Also we…