Related papers: Extending wavelet regularity beyond Gevrey classes
This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups $H < {\rm GL}(3,\mathbb{R})$ that give rise to a continuous wavelet transform with associated irreducible quasi-regular…
The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We propose first a suitable for our purposes…
We discuss the constraints on the Standard Model Effective Field Theory inferred from global fits to electroweak data. Special attention is paid to two unconstrained combinations of Wilson coefficients that are present when the analysis is…
Let $(\eta_i)_{i\geq1}$ be a sequence of $\psi$-mixing random variables. Let $m=\lfloor n^\alpha \rfloor, 0< \alpha < 1, k=\lfloor n/(2m) \rfloor,$ and $Y_j = \sum_{i=1}^m \eta_{m(j-1)+i}, 1\leq j \leq k.$ Set $ S_k^o=\sum_{j=1}^{k } Y_j $…
In this paper we show how to construct a certain class of orthonormal bases in $L^2({\bf R}^d)$ starting from one or more Gabor orthonormal bases in $L^2({\bf R})$. Each such basis can be obtained acting on a single function…
It is of interest to study a wavelet system with a minimum number of generators. It has been showed by X. Dai, D. R. Larson, and D. M. Speegle in [11] that for any $d\times d$ real-valued expansive matrix M, a homogeneous orthonormal…
Extending the principle of local gauge invariance $\psi(x)\to \exp\left(\imath \sum_A \omega^A(x)T^A \right) \psi(x), x \in \mathbb{R}^d$, with $T^A$ being the generators of the gauge group $\mathcal{A}$, to the fields $\psi(g)\equiv…
Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of…
A simple elliptic singularity of type $E_N^{(1,1)}$ ($N=6,7,8$) can be described in terms of a marginal deformation of an invertible polynomial $W$. In the papers \cite{KS} and \cite{MR} the authors proved a mirror symmetry statement for…
We study the decay process of $J/\psi\rightarrow e^+e^- \phi$ where the relatively clean electromagnetic (EM) transitions appear at leading order at tree level while the hadronic contributions only emerge via hadronic loop transitions. We…
Starting from a chiral invariant and quark line rule conserving Lagrangian of pseudoscalar and vector nonets we introduce first and second order symmetry breaking as well as quark line rule violating terms and fit the parameters, at tree…
The decay $\eta'\to\eta\pi^{0}\pi^{0}$ is studied in the framework of isobar model. It is shown, that good agreement with the experiment is achieved if $a_0$- and $\sigma$-meson contributions are taken into account. The contribution of…
The covariant quark model represents an appropriate theoretical framework to describe the recent results on $B_{s}\rightarrow J/\psi+\eta$ and $B_{s}\rightarrow J/\psi+\eta'$ decays from the Belle collaboration. In this article we present…
We give an equivariant version of Packer and Rieffel's theorem on sufficient conditions for the existence of orthonormal wavelets in projective multiresolution analyses. The scaling functions that generate a projective multiresolution…
Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem…
We investigate the sparsity of the Gabor-matrix representation of Fourier integral operators with a phase having quadratic growth. It is known that such an infinite matrix is sparse and well organized, being in fact concentrated along the…
We consider nonparametric Bayesian inference in a reflected diffusion model $dX_t = b (X_t)dt + \sigma(X_t) dW_t,$ with discretely sampled observations $X_0, X_\Delta, \dots, X_{n\Delta}$. We analyse the nonlinear inverse problem…
A new method is presented for the construction of a natural continuous wavelet transform on the sphere. It incorporates the analysis and synthesis with the same wavelet and the definition of translations and dilations on the sphere through…
We present a strong-deflection expansion for the deflection angle of light rays scattered near a degenerate photon sphere in asymptotically flat, static, and spherically symmetric spacetimes. Our prescription isolates the divergent…
The nonlinear semigroup generated by the subdifferential of a convex lower semicontinuous function $\varphi$ has a smoothing effect, discovered by H. Br\'ezis, which implies maximal regularity for the evolution equation. We use this and…