Related papers: A note on twisted discrete singular Radon transfor…
We conjecture a geometrical form of the Paley-Wiener theorem for the Dunkl transform and prove three instances thereof, one of which involves a limit transition from Opdam's results for the graded Hecke algebra. Furthermore, the connection…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
We obtain weak type (1,1) estimates for the inverses of truncated discrete rough Hilbert transform. We include an ex- ample showing that our result is sharp. One of the ingredients of the proof are regularity estimates for convolution of…
In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant.…
We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In $\mathbb{R}^3$ it maps a function to its surface integrals over circular cones, and in $\mathbb{R}^2$ it maps a function to its…
This paper contains an $L^{p}$ improving result for convolution operators defined by singular measures associated to hypersurfaces on the motion group. This needs only mild geometric properties of the surfaces, and it extends earlier…
Semyanistyi's fractional integrals have come to analysis from integral geometry. They take functions on $R^n$ to functions on hyperplanes, commute with rotations, and have a nice behavior with respect to dilations. We obtain sharp…
Quantized contact transforms (QCT) have been constructed in \cite{SKK73}. We give here a complete proof of the fact that such QCT commute with the action of microdifferential operators. To our knowledge, such a proof did not exist in the…
We study a trilinear singular integral form acting on two-dimensional functions and possessing invariances under arbitrary matrix dilations and linear modulations. One part of the motivation for introducing it lies in its large symmetry…
We study spectral approximations of Schr\"odinger operators $T=-\Delta+Q$ with complex potentials on $\Omega=\mathbb{R}^d$, or exterior domains $\Omega\subset \mathbb{R}^d$, by domain truncation. Our weak assumptions cover wide classes of…
A discrete Hubbard-Stratonovich transformation is presented for systems with an orbital degeneracy $N$ and a Hubbard Coulomb interaction without multiplet effects. An exact transformation is obtained by introducing an external field which…
We develop several upper and lower bounds for the $A$-Euclidean operator radius of $2$-tuple operators admitting $A$-adjoint, and show that they refine the earlier related bounds. As an application of the bounds developed here, we obtain…
Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…
In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of…
We discuss the closability of directional derivative operators with respect to a general Radon measure $\mu$ on $\mathbb{R}^d$; our main theorem completely characterizes the vectorfields for which the corresponding operator is closable from…
We study the variation of the discrete spectrum of a bounded non-negative operator in a Krein space under a non-negative Schatten class perturbation of order $p$. It turns out that there exist so-called extended enumerations of discrete…
For a commutative ring $R$, we define the notions of deformed Picard algebroids and deformed twisted differential operators on a smooth, separated, locally of finite type $R$-scheme and prove these are in a natural bijection. We then define…
Given a finite simplicial complex, a unimodular representation of its fundamental group and a closed twisted cochain of odd degree, we define a twisted version of the Reidemeister torsion, extending a previous definition of V. Mathai and S.…
We investigate properties of pseudodifferential operators on $L^2$ space on manifold with ends including asymptotically conical or hyperbolic ends. Our pseudodifferential operators are a generalization of the canonical quantization which…
Singularities of the Radon transform of a piecewise smooth function $f(x)$, $x\in R^n$, $n\geq 2$, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of $f(x)$ are…