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We calculate the least upper bounds of pointwise and uniform approximations for classes of $2\pi$-periodic functions expressible as convolutions of an arbitrary square summable kernel with functions, which belong to the unit ball of the…
We study the growth rate of the inclusion length of an almost periodic function. For a given a. p. function such growth rate depends on the algebraic structure of Fourier exponents, i. e. on how good they can be approximated by rational…
The purpose of this paper is to extend the result of arXiv:1810.00823 to mixed H\"older functions on $[0,1]^d$ for all $d \ge 1$. In particular, we prove that by sampling an $\alpha$-mixed H\"older function $f : [0,1]^d \rightarrow…
One considers a system on $\mathbb{C}^2$ close to an invariant curve which can be viewed as a generalization of the semi-standard map to a trigonometric polynomial with many Fourier modes. The radius of convergence of an analytic…
We use the embedding formalism to study correlation functions of a d-dimensional Euclidean CFT in the presence of a $q$ co-dimensional defect. The defect breaks the global conformal group $SO(d+1,1)$ into $SO(d-q+1,1) \times SO(q)$. We…
One of the most important quantities characterizing the microscopic properties of quantum systems are dynamical correlation functions. These correlations are obtained by time-evolving a perturbation of an eigenstate of the system, typically…
Denote by ${\mathcal D}$ the open unit disc in the complex plane and $\partial {\mathcal D}$ its boundary. Douglas showed through an identical quantity represented by the Fourier coefficients of the concerned function $u$ that…
We present a method for constructing superoscillatory functions the superoscillatory part of which approximates a given polynomial with arbitrarily small error in a fixed interval. These functions are obtained as the product of the…
The goal of this note is to show that continuous functions may be approximated using scattered translates of the Poisson kernel.
In this thesis, we construct a new version of orthogonal calculus for functors $F$ from $C_2$-representations to $C_2$-spaces, where $C_2$ is the cyclic group of order 2. For example, the functor $BO(-)$, which sends a $C_2$-representation…
We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the Linear Delta Expansion. All the results obtained in this article are fully…
In this paper we extend the dichotomy given by Samuelsson and Wold that can be thought of as an analogue of the Wermer maximality theorem in $\mathbb{C}^2$ for certain polynomial polyhedra. We consider complex non-degenerate simply…
We study application of the Clifford algebra and the Grassmann algebra to image recognitions in $(3+1)D$ using quaternions. Following S.L.Adler, we construct a quaternion-valued wave function model with fermions and bosons of equal degrees…
In this paper, we study parallel algorithms for the correlation clustering problem, where every pair of two different entities is labeled with similar or dissimilar. The goal is to partition the entities into clusters to minimize the number…
We investigate the problem of reconstructing a 2D piecewise smooth function from its bandlimited Fourier measurements. This is a well known and well studied problem with many real world implications, in particular in medical imaging. While…
In even-dimensional Euclidean space for integer powers of the Laplacian greater than or equal to the dimension divided by two, a fundamental solution for the polyharmonic equation has logarithmic behavior. We give two approaches for…
The semisimple part of d-dimensional Galilean conformal algebra g^(d) is given by h^(d)=O(2,1)+O(d), which after adding via semidirect sum the 3d-dimensional Abelian algebra t^(d) of translations, Galilean boosts and constant accelerations…
Binary mixtures of hard-spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the…
This paper defines a distance function that measures the dissimilarity between planar geometric figures formed with straight lines. This function can in turn be used in partial matching of different geometric figures. For a given pair of…
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…