相关论文: Fractional integration with singularity on Light-c…
A genuine continuum treatment of the massive \phi^4_{1+1}-theory in light-cone quantization is proposed. Fields are treated as operator valued distributions thereby leading to a mathematically well defined handling of ultraviolet and light…
In this paper, we investigate the behavior of the bounds of the composition for rough singular integral operators on the weighted space. More precisely, we obtain the quantitative weighted bounds of the composite operator for two singular…
New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces.…
We study the Frobenius-Lusztig kernel for quantum affine algebras at root of unity of small orders that are usually excluded in literature. These cases are somewhat degenerate and we find that the kernel is in fact mostly related to…
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…
We find the transition kernels for four Markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin-McGregor type kernel. The resulting kernels all inherit the determinantal…
We prove a useful formula and new properties for the recently introduced power fractional calculus with non-local and non-singular kernels. In particular, we prove a new version of Gronwall's inequality involving the power fractional…
We introduce the concept of fractional derivative of Riemann-Liouville on time scales. Fundamental properties of the new operator are proved, as well as an existence and uniqueness result for a fractional initial value problem on an…
We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…
For alpha in [0,n) we demonstrate the failure of energy reversal for the vector of alpha-fractional Riesz transforms, and more generally for any vector of alpha-fractional convolution singular integrals having a kernel with vanishing…
In this paper we provide a full characterization of linear integral operators acting from the space of functions of bounded Jordan variation to the space of functions of bounded Schramm variation in terms of their generating kernels.
The radially deformed Fourier transform, introduced in [S. Ben Said, T. Kobayashi and B. Orsted, Laguerre semigroup and Dunkl operators, Compositio Math.], is an integral transform that depends on a numerical parameter $a \in R^{+}$. So…
Some aspects of Cauchy integrals on sets with dimension larger than 1 are briefly discussed.
We present a factorized decomposition of 4-point scalar conformal blocks near the lightcone, which applies to arbitrary intermediate spin and general spacetime dimensions. Then we discuss the systematic expansion in large intermediate spin…
We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove that such discrete operators extend to bounded operators from $\ell^p$ to $\ell^q$…
We consider $A_1$-weights and prove weighted weak type $(1,1)$ estimates for oscillatory singular integrals with kernels satisfying a Dini condition.
In this paper we obtain the weak type (1,1) boundedness of Calderon-Zygmund operators acting over operator-valued functions. Our main tools for its solution are a noncommutative form of Calderon-Zygmund decomposition in conjunction with a…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions,…
This is a brief survey of recent results by the authors devoted to one of the most important operators of integral geometry. Basic facts about the analytic family of cosine transforms on the unit sphere and the corresponding Funk transform…