Related papers: Functional Equations and Poincare Invariant Mechan…
Lectures on Poincare invariant quantum theory presented at TJNAF.
We study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. We solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to…
The purpose of this paper is to investigate the following invariance equation involving two $2$-variable generalized Bajraktarevi\'c means, i.e., we aim to solve the functional equation $$…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
We derive a functional change of variable formula for {\it non-anticipative} functionals defined on the space of right continuous paths with left limits. The functional is only required to possess certain directional derivatives, which may…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
The paper considers truncation errors for functions of the form $f(x_1,x_2,\dots)=g(\sum_{j=1}^\infty x_j\,\xi_j)$, i.e., errors of approximating $f$ by $f_k(x_1,\dots,x_k)=g(\sum_{j=1}^k x_j\,\xi_j)$, where the numbers $\xi_j$ converge to…
In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in…
We introduce a natural definition for sums of the form \[ \sum_{\nu=1}^x f(\nu) \] when the number of terms x is a rather arbitrary real or even complex number. The resulting theory includes the known interpolation of the factorial by the…
We construct a measure in the hamiltonian function level sets that is invariant under the hamiltonian flow for short times and flow preserving for arbitrarily long times. This allows a probabilistic approach to the study of hamiltonian…
The partial Hamiltonian systems of the form $\dot q^i=\frac{\partial H}{\partial p_i}, \dot p^i=-\frac{\partial H}{\partial q_i}+\Gamma^i(t,q^i,p_i)$ arise widely in different fields of the applied mathematics. The partial Hamiltonian…
Given a semigroup $S$ generated by its squares, we determine the complex-valued solutions of the following system of cosine-sine functional equations \begin{align*} f(xy)=f(x)g_{1}(y)+g_{1}(x)f(y)+\lambda_{1}^{2}\,h(x)h(y),\; x,y\in S,\\…
In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.
In this note we study $SL(2,\mathbb{Z})$-invariant functions such as modular graph functions or coefficient functions of higher derivative corrections in type IIB string theory. The functions solve inhomogeneous Laplace equations and we…
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…
We study the product formula $(fg)(A) = f(A)g(A)$ in the framework of (unbounded) functional calculus of sectorial operators $A$. We give an abstract result, and, as corollaries, we obtain new product formulas for the holomorphic functional…
We study the end-behavior of integer-valued FI-modules. Our first result describes the high degrees of an FI-module in terms of newly defined tail invariants. Our main result provides an equivalence of categories between FI-tails and…