Related papers: Effective Pruefer Angles and Relative Oscillation …
A key advantage of isogeometric discretizations is their accurate and well-behaved eigenfrequencies and eigenmodes. For degree two and higher, however, optical branches of spurious outlier frequencies and modes may appear due to boundaries…
We give an effective criterion for the identifiability of additive decompositions of homogeneous forms of degree $d$ in a fixed number of variables. Asymptotically for large $d$ it has the same order of the Kruskal's criterion adapted to…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
In this study, a formula for regularized sums of eigenvalues of a Sturm-Liouville problem with retarded argument at the point of discontinuity is obtained. Moreover, oscillation properties of the related problem is investigated.
Inverse spectral problems for Sturm-Liouville operators on a finite interval with non-separated boundary conditions are studied in the central symmetric case, when the potential is symmetric with respect to the middle of the interval. We…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…
We establish anisotropic uncertainty principles (UPs) for general metaplectic operators acting on $L^2(\mathbb{R}^d)$, including degenerate cases associated with symplectic matrices whose $B$-block has nontrivial kernel. In this setting,…
We introduce two a posteriori error estimators for N\'ed\'elec finite element discretizations of the curl-curl problem. These estimators pertain to a new Prager-Synge identity and an associated equilibration procedure. They are reliable and…
We consider a class of H\"ormander-type oscillatory integral operators in $\mathbb{R}^n$ for $n \geq 3$ odd with real analytic phase. We derive weak conditions on the phase which ensure $L^p$ bounds beyond the universal $p \geq 2 \cdot…
In this paper, we establish the sharp criteria for the nonexistence of positive solutions to the Hardy-Littlewood-Sobolev (HLS) type system of nonlinear equations and the corresponding nonlinear differential systems of Lane-Emden type…
In this article I study different possibilities of analytically solving the Sturm-Liouville problem with variable coefficients of sufficiently arbitrary behavior with help of perturbation theory. I show how the problem can be reformulated…
The method of second order relative spectra has been shown to reliably approximate the discrete spectrum for a self-adjoint operator. We extend the method to normal operators and find optimal convergence rates for eigenvalues and…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
Matrix perturbation bounds (such as Weyl and Davis-Kahan) are used abundantly in many areas of mathematics and data science. Many bounds (such as the above two) involve the spectral norm of the noise matrix and are sharp in worst case…
We comparatively use some classical spectral collocation methods as well as highly performing Chebfun algorithms in order to compute the eigenpairs of second order singular Sturm-Liouville problems with separated self-adjoint boundary…
We prove estimates for the variation of the eigenvalues of uniformly elliptic operators with homogeneous Dirichlet or Neumann boundary conditions upon variation of the open set on which an operator is defined. We consider operators of…
We prove some new results which justify the use of interval truncation as a means of regularising a singular fourth order Sturm-Liouville problem near a singular endpoint. Of particular interest are the results in the so called lim-3 case,…
Pr\"ufer variables are a standard tool in spectral theory, developed originally for perturbations of the free Schr\"odinger operator. They were generalized by Kiselev, Remling, and Simon to perturbations of an arbitrary Schr\"odinger…
We provide a justification with rigorous error estimates showing that the leading term in weakly nonlinear geometric optics expansions of highly oscillatory reflecting pulses is close to the uniquely determined exact solution for small…