Related papers: The Borel-Ritt problem in Beurling ultraholomorphi…
We prove several improved versions of the Borel-Ritt theorem about the surjectivity of the asymptotic Borel mapping in classes of functions with $\boldsymbol{M}$-uniform asymptotic expansion on an unbounded sector of the Riemann surface of…
We characterize the surjectivity and the existence of a continuous linear right inverse of the Stieltjes moment mapping on Gelfand-Shilov spaces, both of Beurling and Roumieu type, in terms of their defining weight sequence. As a corollary,…
The Borel map takes a smooth function to its infinite jet of derivatives (at zero). We study the restriction of this map to ultradifferentiable classes of Beurling type in a very general setting which encompasses the classical…
We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at…
We study the injectivity and surjectivity of the Borel map in three instances: in Roumieu-Carleman ultraholomorphic classes in unbounded sectors of the Riemann surface of the logarithm, and in classes of functions admitting, uniform or…
We study the surjectivity of, and the existence of right inverses for, the asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences in the sense of E. M. Dyn'kin. We extend previous results by J.…
We prove sectorial extension theorems for ultraholomorphic function classes of Beurling type defined by weight functions with a controlled loss of regularity. The proofs are based on a reduction lemma, due to the second author, which allows…
It is developed the theory of the Dirichlet problem for harmonic functions. On this basis, for the nondegenerate Beltrami equations in the quasidisks and, in particular, in the smooth domains, it is proved the existence of regular solutions…
We address an open problem posed by H. Brezis, M. Marcus and A.C. Ponce in: Nonlinear elliptic equations with measures revisited. In: Mathematical Aspects of Nonlinear Dispersive Equations (J. Bourgain, C. Kenig, S. Klainerman, eds.),…
We prove an extension theorem for ultraholomorphic classes defined by so-called Braun-Meise-Taylor weight functions and transfer the proofs from the single weight sequence case from V. Thilliez [28] to the weight function setting. We are…
We derive the solvability and regularity of the Dirichlet problem for fully non-linear elliptic equations possibly with degenerate right-hand side on Hermitian manifolds, through establishing a quantitative version of boundary estimate…
For a set $X\sbst\R$, let $B(X)\sbst\R^X$ denote the space of Borel real-valued functions on $X$, with the topology inherited from the Tychonoff product $\R^X$. Assume that for each countable $A\sbst B(X)$, each $f$ in the closure of $A$ is…
A new construction of linear continuous right inverses for the asymptotic Borel map is provided in the framework of general Carleman ultraholomorphic classes in narrow sectors. Such operators were already obtained by V. Thilliez by means of…
We construct optimal flat functions in Carleman-Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitably restricted opening. A general procedure is presented in…
The present paper establishes the first result on the absolute continuity of elliptic measure with respect to the Lebesgue measure for a divergence form elliptic operator with non-smooth coefficients that have a BMO anti-symmetric part. In…
Let $X$ be a (real or complex) rearrangement-in\-va\-riant function space on $\Om$ (where $\Om = [0,1]$ or $\Om \subseteq \bbN$) whose norm is not proportional to the $L_2$-norm. Let $H$ be a separable Hilbert space. We characterize…
We study the Borel map, which maps infinitely differentiable functions on an interval to the jets of their Taylor coefficients at a given point in the interval. Our main results include a complete description of the image of the Borel map…
We construct a global geometric model for the bosonic sector and Killing spinor equations of four-dimensional $\mathcal{N}=1$ supergravity coupled to a chiral non-linear sigma model and a Spin$^{c}_0$ structure. The model involves a…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
This paper produces explicit strongly Hermitian Einstein-Maxwell solutions on the smooth compact $4$-manifolds that are $S^2$-bundles over compact Riemann surfaces of any genus. This generalizes the existence results by C. LeBrun in…