Related papers: A continuous spherical wavelet transform for~$\mat…
We construct families of smooth functions $H\colon\mathbb{R}^{n+1}\to\mathbb{R}$ such that the Euclidean $(n+1)$-space is completely filled by not necessarily round hyperspheres of mean curvature $H$ at every point.
Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and…
We construct a Continuous Wavelet Transform (CWT) on the torus $\mathbb T^2$ following a group-theoretical approach based on the conformal group $SO(2,2)$. The Euclidean limit reproduces wavelets on the plane $\mathbb R^2$ with two…
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of…
The eigenfamilies of Gudmundsson and Sakovich can be used to generate harmonic morphisms, proper $r$-harmonic maps, and minimal co-dimension $2$ submanifolds. This article begins by characterising the globally defined eigenfamilies of the…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the…
We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely…
An inverse cascade - energy transfer to progressively larger scales - is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and…
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…
The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This…
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…
In this paper, we exploit the theory of convolution of index Whittaker transform for study of continuous and discrete Index Whittaker wavelet transform and discuss some of its basic properties. Certain boundedness, Plancherel as well as…
The application of the continuous wavelet transform to study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies due to the admissibility condition. We propose an alternative…
In this paper, we have studied continuous fractional wavelet transform (CFrWT) in $n$-dimensional Euclidean space $\mathbb{R}^n$ with dilation parameter $\boldsymbol a=(a_{1},a_{2},\ldots,a_{n}),$ such that none of $a_{i}'s$ are zero.…
In this paper, we are concerned with $n$-dimensional spherical wavelets derived from the theory of approximate identities. For nonzonal bilinear wavelets introduced by Ebert \emph{et al.} in 2009 we prove isometry and Euclidean limit…
The spectral properties of the Ruelle transfer operator which arises from a given polynomial wavelet filter are related to the convergence question for the cascade algorithm for approximation of the corresponding wavelet scaling function.
We describe local and global properties of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand-Shilov type spaces and their duals. In…
We consider the smooth inverse mean curvature flow of strictly convex hypersurfaces with boundary embedded in $\mathbb{R}^{n+1},$ which are perpendicular to the unit sphere from the inside. We prove that the flow hypersurfaces converge to…