Related papers: Positive Functionals Induced by Minimizers of Caus…
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…
The Lagrangian of the causal action principle is computed in Minkowski space for Dirac wave functions interacting with classical electromagnetism and linearized gravity in the limiting case when the ultraviolet cutoff is removed. Various…
The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantizations. General features of time-independent Wigner functions…
Noncommutative space has been found to be of use in a number of different contexts. In particular, one may use noncommutative spacetime to generate quantised gravity theories. Via an identification between the Moyal $\star$-product on…
The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_j(Y_j - {\mu}(t_j))^2 + {\lambda}\int_a^b [{\mu}"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,..., n$. The…
We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a…
We prove the existence of minimizers in the class of negative definite measures on compact subsets of momentum space in the homogeneous setting under several side conditions (constraints). The method is to employ Prohorov's theorem. Given a…
We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on $\mathbb{R}$, we define fractional operators by means of a functional calculus…
We give a local characterization of the class of functions having positive distributional derivative with respect to $\bar{z}$ that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild non-degeneracy…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
We study a nonlocal perimeter functional inspired by the Minkowski content, whose main feature is that it interpolates between the classical perimeter and the volume functional. This problem is related by a generalized coarea formula to a…
In the article, some bilinear evolution equations in Hilbert space driven by paths of low regularity are considered and solved explicitly. The driving paths are scalar-valued and continuous, and they are assumed to have a finite $p$-th…
In the theory of causal fermion systems, the physical equations are obtained as the Euler-Lagrange equations of a causal variational principle. Studying families of critical measures of causal variational principles, a class of conserved…
In this paper we consider a class of time-dependent neutral stochastic functional differential equations with finite delay driven by a fractional Brownian motion in a Hilbert space. We prove an existence and uniqueness result for the mild…
We prove an a priori estimate for the second derivatives of local minimizers of integral functionals of calculus of variation with convex integrand with respect to the gradient variable, assuming that the function that measures the…
Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…
Asymptotically flat static causal fermion systems are introduced. Their total mass is defined as a limit of surface layer integrals which compare the measures describing the asymptotically flat spacetime and a vacuum spacetime near spatial…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
This paper deals with a linear model of regression on quantiles when the explanatory variable takes values in some functional space and the response is scalar. We propose a spline estimator of the functional coefficient that minimizes a…
The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The…