Related papers: The functional integral with unconditional Wiener …
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…
We prove an integration by parts formula on the law of the reflecting Brownian motion $X:=|B|$ in the positive half line, where $B$ is a standard Brownian motion. In other terms, we consider a perturbation of $X$ of the form $X^\epsilon =…
This paper presents a novel generic asymptotic expansion formula of expectations of multidimensional Wiener functionals through a Malliavin calculus technique. The uniform estimate of the asymptotic expansion is shown under a weaker…
We study the boundary continuity of solutions to fully nonlinear elliptic equations. We first define a capacity for operators in non-divergence form and derive several capacitary estimates. Secondly, we formulate the Wiener criterion, which…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
In this paper, we obtain some formulas for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. By using these formulas, we give new closed form sums of several quadratic Euler series through Riemann zeta…
Let $b_d$ be the Weyl symbol of the inverse to the harmonic oscillator on $\R^d$. We prove that $b_d$ and its derivatives satisfy convenient bounds of Gevrey and Gelfand-Shilov type, and obtain explicit expressions for $b_d$. In the…
Following [14] and [12], we formalize the notion of an oscillatory integral interpreted as a functional on the amplitudes supported near a fixed critical point $x_0$ of the phase function with zero critical value. We relate to an…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…
A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can…
Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function…
Wiener's criterion for the regularity of a boundary point with respect to the Dirichlet problem for the Laplace equation has been extended to various classes of elliptic and parabolic partial differential equations. They include linear…
Starting with the representation of the Wilson average in the Euclidean 4D compact QED as a partition function of the Universal Confining String Theory, we derive for it the corresponding loop equation, alternative to the familiar one. In…
We give a variational formulation for $-\log\mathbb{E}_\nu\left[e^{-f}|\mathcal{F}_t\right]$ for a large class of measures $\nu$. We give a refined entropic characterization of the invertibility of some perturbations of the identity. We…
We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
In the present paper a method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. Starting with the problem of a reflection from an impenetrable wall, the obtained solution is then…
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…
We consider the limit set of generalised iterated function systems. Under the assumption of a natural potential, the so called cylinder function, we prove the existence of the invariant probability measure satisfying the equilibrium state.…
I review the generating function for quantum-statistical mechanics, known as the Feynman-Vernon influence functional, the decoherence functional, or the Schwinger-Keldysh path integral. I describe a probability-conserving $i\varepsilon$…