Related papers: Restriction theorem for the Fourier-Dunkl transfor…
We prove the Plancherel formula for a four-parameter family of discrete Fourier transforms and their multivariate generalizations stemming from corresponding generalized Schur polynomials. For special choices of the parameters, this…
We present a generalization of Brouwer's conjectural family of inequalities -- a popular family of inequalities in spectral graph theory bounding the partial sum of the Laplacian eigenvalues of graphs -- for the case of abstract simplicial…
Recent advances have extended the Dunkl transform to the setting of Clifford algebras. In particular, the two-sided quaternionic Dunkl transform has been introduced as a Dunkl analogue of the two-dimensional quaternionic Fourier transform.…
Dunkl theory is a far reaching generalization of Fourier analysis and special function theory related to root systems. During the sixties and seventies, it became gradually clear that radial Fourier analysis on rank one symmetric spaces was…
We prove $L^p$ norm convergence for (appropriate truncations of) the Fourier series arising from the Dirichlet Laplacian eigenfunctions on three types of triangular domains in $\mathbb{R}^2$: (i) the 45-90-45 triangle, (ii) the equilateral…
We define a scalar valued Fourier transform for functions on the Heisenberg group and establish some of its basic properties like inversion formula, Plancherel theorem and Riemann-Lebesgue lemma. We also restate certain well known theorems…
We prove a Fourier restriction estimate under the assumption that certain convolution power of the measure admits an $r$-integrable density.
We consider the Fourier restriction operators associated to certain degenerate curves in R^d for which the highest torsion vanishes. We prove estimates with respect to affine arclength and with respect to the Euclidean arclength measure on…
Let $G$ be a (split) reductive group over $\mathbb{F}_q$, and let $M$ be a standard Levi subgroup of $G$. Consider $P$ and $P'$ parabolics in $G$, containing $M$, with Levi factor $M$. we let $U = R_u(P)$ (resp., $U' = R_u(P')$) denote the…
The Katz-Sarnak density conjecture states that, in the limit as the conductors tend to infinity, the behavior of normalized zeros near the central point of families of L-functions agree with the N -> oo scaling limits of eigenvalues near 1…
We construct a collection of higher Chow cycles on certain surfaces which degenerate to an arrangement of planes in general position. When its degree is 4, this construction gives a new explicit proof of the Hodge-D-Conjecture for a certain…
We extend the estimates for maximal Fourier restriction operators proved by M\"{u}ller, Ricci, and Wright in \cite{MR3960255} and Ramos in \cite{MR4055940} to the case of arbitrary convex curves in the plane, with constants uniform in the…
We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature $F$, where the defining cone of $F$ is $\C_+$. $F$ is only assumed to…
We prove a bound on the sum of the product of curl-free and divergence-free vector fields. Under appropriate orthonormality conditions our bound scales sublinearly in the number of terms, similar in spirit to Lieb--Thirring inequalities.
In this paper, we showed that for suitable $(\beta,p, s,\ell)$ the $\beta$-order fractional derivative with respect to the last coordinate of the Fourier transform of an $L^p(\mathbb{R}^n)$ function is in $H^{-s}$ after restricting to a…
The construction of a multiresolution analysis starts with specification of a scale function. The Fourier transform of this function is defined by an infinite product. The convergence of this product is usually discussed in the context of…
We generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of graph(F)\cup(\partial D\times D) -- where D is the open unit disc and graph(F) denotes the graph of a continuous D-valued function F -- to the…
The Fourier transforms of polyhedral cones can be used, via Brion's theorem, to compute various geometric quantities of polytopes, such as volumes, moments, and lattice-point counts. We present a novel method of computing these conic…
We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, based on the theory of conformal restriction. This is a mathematical theory that was recently…
This paper is devoted to the $L^p(\mathbb R)$ theory of the fractional Fourier transform (FRFT) for $1\le p < 2$. In view of the special structure of the FRFT, we study FRFT properties of $L^1$ functions, via the introduction of a suitable…