Related papers: Continuous wavelet transforms on $n$-dimensional s…
A new method of connecting two wavelet sets with a continuous path of wavelet sets is given. The method is based on a pure set theoretic fact known as the Schroder-Cantor-Bernstein theorem and on a characterization of wavelet sets in terms…
In 1953, Blumenthal showed that every semi-metric space that is isometrically embeddable in a Hilbert space has the n-point property; we have previously called such spaces supermetric spaces. Although this is a strictly stronger property…
The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…
We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equation to space forms and reflects various geometric properties…
A low frequency approximation of the discrete Sommerfeld diffraction problems, involving the scattering of a time harmonic lattice wave incident on square lattice by a discrete Dirichlet or a discrete Neumann half-plane, is investigated. It…
In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible function by applying the unitary operators associated to a…
Let X and Y be planar Jordan domains of the same finite connectivity, Y being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h:X->Y in the Sobolev space $W^{1,2}$ extends to a continuous map between closed domains.…
The main purpose of this short note is to present an adaptation of the multilinear Bellman function technique from [4] to the time-frequency analysis. Demeter and Thiele introduced the two-dimensional bilinear Hilbert transform in [3] and…
Continuous wavelet transforms arising from the quasiregular representation of a semidirect product of a vector group with a matrix group -- the so-called dilation group -- have been studied by various authors. Recently the attention has…
Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behavior, yet that wave behavior disappears when one tries to determine the particle's path inside the interferometer. This idea has been…
Relation of ultrametric analysis, wavelet theory and cascade models of turbulence is discussed. We construct the explicit solutions for the nonlinear ultrametric integral equation with quadratic nonlinearity. These solutions are built by…
Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance…
We establish variational estimates related to the problem of restricting the Fourier transform of a three-dimensional function to the two-dimensional Euclidean sphere. At the same time, we give a short survey of the recent field of maximal…
The paper is devoted to some of the difficulties which the Wheeler - DeWitt quantum geometrodynamics encountered, in particular, a strong mathematical proof that this theory is gauge-invariant, the definition of the wave function of the…
We find a new class of solutions that are traveling waves on the boundary of two--dimensional droplet of ideal fluid. We assume that the free surface is subject only to the force of surface tension, and the fluid flow is potential. We use…
By using the Bergman representative coordinate and Calabi's diastasis, we extend a theorem of Lu to bounded pseudoconvex domains whose Bergman metric is incomplete with constant holomorphic sectional curvature. We characterize such domains…
The "Perpendicular Bisectors Construction" is a natural way to seek a replacement for the circumcenter of a noncyclic quadrilateral in the plane. In this paper, we generalize this iterative construction to a construction on polytopes with…
In 1996 Chui and Wang proved that the uncertainty constants of scaling and wavelet functions tend to infinity as smoothness of the wavelets grows for a broad class of wavelets such as Daubechies wavelets and spline wavelets. We construct a…
In this paper we use the concept of wavelet sets as introduced by X. Dai and D. Larson, to decompose the wavelet representation of the discrete group associated to an arbitrary $n \times n$ integer dilation matrix as a direct integral of…
We prove discrete-to-continuum convergence of interaction energies defined on lattices in the Euclidean space (with interactions beyond nearest neighbours) to a crystalline perimeter, and we discuss the possible Wulff shapes obtainable in…