Related papers: The vector-valued Stieltjes moment problem with ge…

One of the classical problems concerns the class of analytic functions $f$ on the open unit disk $|z|<1$ which have finite Dirichlet integral $\Delta(1,f)$, where $$\Delta(r,f)=\iint_{|z|<r}|f'(z)|^2 \, dxdy \quad (0<r\leq 1). $$ The class…

Given a periodic function $f$, we study the convergence almost everywhere and in norm of the series $\sum_{k} c_k f(kx)$. Let $f(x)= \sum_{m=1}^\infty a_m \sin {2\pi m x}$ where $\sum_{m=1}^\infty a_{m }^2d(m) <\infty$ and $d(m)=\sum_{d|m}…

We introduce and study the approximation properties of $g$-polynomials, defined as linear combinations of iterated Stieltjes integrals of a constant function. Focusing on the case where the derivator $g$ has finitely many discontinuities,…

The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points…

In this work we extend the theory of Stieltjes systems beyond the monotone case, establishing new chain rules, generalized versions of the Fundamental Theorem of Calculus, compactness tools for Peano-type results, and a $g$-exponential for…

The present paper is devoted to the study of the Dirichlet problem ${\rm{Re}}\,\omega(z)\to\varphi(\zeta)$ as $z\to\zeta,$ $z\in D,\zeta\in \partial D,$ with continuous boundary data $\varphi :\partial D\to\mathbb R$ for Beltrami equations…

We consider Einstein Gravity coupled to dynamical matter consisting of a gauge field with any compact gauge group and minimally coupled scalar fields. We investigate the conditions under which a free specification of a spatial field…

This is the first of a series of papers on the interior regularity of fully nonlinear degenerate elliptic equations. We consider a stochastic optimal control problem in which the diffusion coefficients, drift coefficients and discount…

The paper addresses the exact evaluation of the generalized Stieltjes transform $S_{n}[f]=\int_0^{\infty} f(x) (\omega+x)^{-n}\mathrm{d}x$ of integral order $n=1,2, 3,\dots$ about $\omega =0$ from which the asymptotic behavior of $S_{n}[f]$…

The paper is to reveal the direct links between the well known Sylvester equation in matrix theory and some integrable systems. Using the Sylvester equation $\boldsymbol{K} \boldsymbol{M}+\boldsymbol{M} \boldsymbol{K}=\boldsymbol{r}\,…

Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R,C) to give a new proof of classical Montel's theorem, about continuous solutions of Fr\'{e}chet's functional equation…

In this paper we study the exponential functionals of the processes $X$ with independent increments , namely $$I_t= \int _0^t\exp(-X_s)ds, _,\,\, t\geq 0,$$ and also $$I_{\infty}= \int _0^{\infty}\exp(-X_s)ds.$$ When $X$ is a…

We consider the regularity of the extremal solution of the nonlinear eigenvalue problem (S)_\lambda \qquad {rcr} -\Delta u + c(x) \cdot \nabla u &=& \frac{\lambda}{(1-u)^2} \qquad {in $ \Omega$}, u &=& 0 \qquad {on $ \pOm$}, where $ \Omega…

We study existence, uniqueness and regularity of solutions for ordinary differential equations with infinitely many derivatives such as (linearized versions of) nonlocal field equations of motion appearing in particle physics, nonlocal…

This paper is concerned with a class of generalized slice Fueter-regular functions on arbitrary domains in O with local stem functions. Some classical theorems such as the maximum modulus principle will be generalized to our setting. Some…

We study the Dirichlet problem for the stationary Schr\"odinger fractional Laplacian equation $(-\Delta)^s u + V u = f$ posed in bounded domain $ \Omega \subset \mathbb R^n$ with zero outside conditions. We consider general nonnegative…

A linear operator $S$ in a complex Hilbert space $\hh$ for which the set $\dzn{S}$ of its $C^\infty$-vectors is dense in $\hh$ and $\{\|S^n f\|^2\}_{n=0}^\infty$ is a Stieltjes moment sequence for every $f \in \dzn{S}$ is said to generate…

We prove the monotonicity of positive solutions to the problem $-\Delta u = f(u)$ in $\mathbb{R}^N_+ := \{(x',x_N)\in\mathbb{R}^N \mid x_N>0 \}$ under zero Dirichlet boundary condition with a possible singular nonlinearity $f$. In some…

In this work, we introduce new integral formulations based on the convolution quadrature method for the time-domain modeling of perfectly electrically conducting scatterers that overcome some of the most critical issues of the standard…

The purpose of this work is to analyze the wellposedness and the blow-up of solutions of the higher-order parabolic semilinear equation \[ u_t+(-\Delta)^{d}u=|x|^{\alpha}|u|^{p}+\zeta(t){\mathbf w}(x) \ \quad\mbox{for }…