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Functionals of Brownian/non-Brownian motions have diverse applications and attracted a lot of interest of scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of…

In this paper we aim for a generalisation of the Steenrod Approximation Theorem from, concerning a smoothing procedure for sections in smooth locally trivial bundles. The generalisation is that we consider locally trivial smooth bundles…

Many applications require stochastic processes specified on two- or higher-dimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational…

We establish an integral test describing the exact cut-off between recurrence and transience for normally reflected Brownian motion in certain unbounded domains in a class of warped product manifolds. Besides extending a previous result by…

The functional equation f(p(z))=g(q(z)) is studied, where p,q are polynomials and f,g are trancendental meromorphic functions in C. We find all the pairs p,q for which there exist nonconstant f,g satisfying our equation and there exist no…

Wick's theorem provides a connection between time ordered products of bosonic or fermionic fields, and their normal ordered counterparts. We consider a generic pair of operator orderings and we prove, by induction, the theorem that relates…

We introduce a new class of nonlocal kinetic equations and nonlocal Fokker-Planck equations associated with an effective generalized thermodynamical formalism. These equations have a rich physical and mathematical structure that can…

We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional L\'{e}vy's modulus of continuity and many other results are its particular cases.…

Some aspects of adelic generalized functions, as linear continuous functionals on the space of Schwartz-Bruhat functions, are considered. The importance of adelic generalized functions in adelic quantum mechanics is demonstrated. In…

Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty…

In this paper, the notion of $\mathbb{C}$-simulation function is introduced and the existence and uniqueness of common fixed points of two self-mappings satisfying contractive conditions in the setting of complex valued metric spaces via…

We prove Banach, Newton-Raphson and Brouwer fixed point theorems in the framework of generalized smooth functions, a minimal extension of Colombeau's theory (and hence of classical distribution theory) which makes it possible to model…

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…

Convolution admits a natural formulation as a functional operation on matrices. Motivated by the functional and entrywise calculi, this leads to a framework in which convolution defines a matrix transform that preserves positivity. Within…

The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…

We prove that the generalized Carleson operator $C_d$ with polynomial phase function is of strong type $(p,r)$, $1<r<p<\infty$; this yields a positive answer in the $1<p<2$ case to a conjecture of Stein which asserts that for $1<p<\infty$…

We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as $(\theta, T)$-periodic functions, and prove several properties and inequalities related to the Fourier transform, including a type…

In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new…

This paper reviews the formulation of the Feynman-Vernon model of linear dissipative systems for a standard Brownian particle moving in an external potential $V(x,t)$ and introduces the formulation of a generalized oscillator model of a…

In this paper, we first construct generalized $q^2$-cosine, $q^2$-sine and $q^2$-exponential functions. We then use $q^2$-exponential function in order to define and investigate a $q^2$-Fourier transform. We establish $q$-analogues of…