Related papers: Constructing functions with prescribed pathwise qu…
We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at…
We consider the problem of constructing a regression model with a functional predictor and a functional response. We extend the functional linear model to the quadratic model, where the quadratic term also takes the interaction between the…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
We construct path integral representations for the evolution operator of q-oscillators with root of unity values of q-parameter using Bargmann-Fock representations with commuting and non-commuting variables, the differential calculi being…
We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative cases. This allows us to define a motivic Fourier transformation for which we get…
We compute the Donaldson-Thomas invariants of a local elliptic surface with section. We introduce a new computational technique which is a mixture of motivic and toric methods. This allows us to write the partition function for the…
We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to H\"ormander's support theorem for…
The paper develops a calculus for a class of real-valued functions having a quadratic variation. The main result is a solution of the representation problem for a class of evolutions having a quadratic variation. The result is applied to…
We construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according to rank; one of the variances is allowed to vanish, but not…
The numerical analysis of variational integrators relies on variational error analysis, which relates the order of accuracy of a variational integrator with the order of approximation of the exact discrete Lagrangian by a computable…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
This paper investigates existence results for path-dependent differential equations driven by a H{\"o}lder function where the integrals are understood in the Young sense. The two main results are proved via an application of Schauder…
Recent innovations in the differential calculus for functions of non-commuting variables, beginning with a quaternionic variable, are now extended to consider some integration.
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
The motivation of this paper is to construct the theory of vector calculus of multivariate arithmetical functions. We prove analogues of integral theorems and Poincare's lemma.
This paper is devoted to a study of mathematical structures arising from choice functions satisfying the path independence property (Plott functions). We broaden the notion of a choice function by allowing of empty choice. This enables us…
We study the restriction of the Fourier transform to quadratic surfaces in vector spaces over finite fields. In two dimensions, we obtain the sharp result by considering the sums of arbitrary two elements in the subset of quadratic surfaces…
We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting we are able to define an analogue of the distributional differential and on finite…
This paper introduces a direct differentiation-based framework that unifies the derivation of influence functions across parametric, nonparametric, and semiparametric models. We show that the Riesz representer of the functional derivative…
This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…