Related papers: Jump formulas for singular integrals and layer pot…
We present a general framework for accurately evaluating finite difference operators in the presence of known discontinuities across an interface. Using these techniques, we develop simple-to-implement, second-order accurate methods for…
A class of (possibly) degenerate stochastic integro-differential equations of parabolic type is considered, which includes the Zakai equation in nonlinear filtering for jump diffusions. Existence and uniqueness of the solutions are…
Claims about recursive self-improvement in AI often slide from repeated internal revision to the possibility of qualitatively stronger capability without clearly distinguishing the underlying computational regimes. This paper gives a formal…
Pointwise estimates for the gradient of solutions to the $p$-Laplace system with right-hand side in divergence form are established. They enable us to develop a nonlinear counterpart of the classical Calder\'on-Zygmund theory in terms of…
A formula for the jumping numbers of a curve unibranch at a singular point is established. The jumping numbers are expressed in terms of the Enriques diagram of the log resolution of the singularity, or equivalently in terms of the…
The ellipsoidal superpotential of the complex projective plane can be interpreted as a count of rigid rational plane curves of a given degree with one prescribed cusp singularity. In this note we present a closed formula for these counts as…
This letter derives some new exponential bounds for discrete time, real valued, conditionally symmetric martingales with bounded jumps. The new bounds are extended to conditionally symmetric sub/ supermartingales, and they are compared to…
In this paper, we establish jump and variational inequalities for the Calder\'{o}n commutators, which are typical examples of non-convolution Calder\'on-Zygmund operators. For this purpose, we also show jump and variational inequalities for…
In this paper, we consider a kind of singular integral which can be viewed as an extension of the classical Calder$\acute{\rm o}$n-Zygmund type singular integral. We establish an estimate of the singular integral in the $L^q$ space for…
This paper presents a quadrature method for evaluating layer potentials in two dimensions close to periodic boundaries, discretized using the trapezoidal rule. It is an extension of the method of singularity swap quadrature, which recently…
In this paper we make a systematic study of the multiplicity of the jumping points associated to the mixed multiplier ideals of a family of ideals in a complex surface with rational singularities. In particular we study the behaviour of the…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
In this paper we construct layer potentials for elliptic differential operators using the Lax-Milgram theorem, without recourse to the fundamental solution; this allows layer potentials to be constructed in very general settings. We then…
This is an expository paper on the characterization of the even (or odd) smooth homogeneous convolution Calder\'on-Zygmund operators in R^n such that the maximal singular integral can be controlled in the L^2 norm by the singular integral.…
This paper gives the recursion formula for mixed multiplicities of maximal degrees with respect to joint reductions of ideals, which is one of important results in the mixed multiplicity theory. Using this result, we give consequences on…
This article shows that for unitary dual reductive pairs the first occurrence of theta lift of an irreducible cuspidal automorphic representation is irreducible. It also proves a refined tower property for theta lifts and the involutive…
The aim of this paper is to prove a theorem of C.~Miranda for the single and double layer potential corresponding to the fundamental solution of a second order differential operator with constant coefficients in Schauder spaces in the…
We establish an integration by parts formula based on jumps times in an abstract framework in order to study the regularity of the law for processes solution of stochastic differential equations with jumps.
We define a natural notion of the singular strata for harmonic maps into $F$-connected complexes (which include locally finite Euclidean buildings), and prove the rectifiability of these strata. We additionally establish bounds on the…
This paper gives an explicit formula for the Ehrhart quasi-polynomial of certain 2-dimensional polyhedra in terms of invariants of surface quotient singularities. Also, a formula for the dimension of the space of quasi-homogeneous…