Related papers: Phi-transform on domains
The aim of this paper is to study properties of Besov-type spaces with variable smoothness. We show that these spaces are characterized by the phi-transforms in appropriate sequence spaces and we obtain atomic decompositions for these…
The objective of this article is to describe a construction of Parseval bandlimited and localized frames on sub-Riemannian compact homogeneous manifolds.
The objective of this paper is to characterize harmonic Hardy spaces and a boundary behavior of harmonic functions on a smooth domain in real Euclidean space.
We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…
The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected, non-complete, unbounded metric spaces by using conformal…
The concept of quasi-affine frame in Euclidean spaces was introduced to obtain translation invariance of the discrete wavelet transform. We extend this concept to a local field $K$ of positive characteristic. We show that the affine system…
This paper is concerned with problems in the context of the theoretical foundation of adaptive (wavelet) algorithms for the numerical treatment of operator equations. It is well-known that the analysis of such schemes naturally leads to…
The present paper is concerned with new Besov-type space of variable smoothness. Nonlinear spline-approximation approach is used to give atomic decomposition of such space. Characterization of the trace space on hyperplane is also obtained.
Although deep neural networks have achieved remarkable results for the task of semantic segmentation, they usually fail to generalize towards new domains, especially when performing synthetic-to-real adaptation. Such domain shift is…
Highly localized kernels constructed by orthogonal polynomials have been fundamental in recent development of approximation and computational analysis on the unit sphere, unit ball and several other regular domains. In this work we first…
In this paper, we study the geometry of bounded domains with piecewise smooth boundary. Specifically, we obtain the relationship between the squeezing function corresponding to polydisk and Levi flatness on bounded generic convex domains.…
In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…
We show that one can characterize the Besov spaces on a smooth compact oriented Riemannian manifold, for the full range of indices, through a knowledge of the size of frame coefficients, using the frames we have constructed in [8].
The objective of the paper is to describe Besov spaces on general compact Riemannian manifolds in terms of the best approximation by eigenfunctions of elliptic differential operators.
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
We study proper holomorphic mappings between strictly pseudoconvex domains with low boundary regularity.
In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame…
We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its…
We present some results dealing with the local geometry of almost complex manifolds. We establish mainly the complete hyperbolicity of strictly pseudoconvex domains, the extension of plurisubharmonic functions through generic submanifolds…
The spherical nature of the wavefronts exhibited in the near-field of antenna arrays enables advanced beamforming capabilities, such as beampointing and beamnulling. In this paper, we exploit these properties to design a near-field beam…