Related papers: The Newman--Shapiro problem
The space of entire functions which are integrable with respect to the Gaussian weight, known also as the Fock space, is one of the preferred functional Hilbert spaces for modelling and experimenting harmonic analysis, quantum mechanics or…
We extend the de Branges-Beurling theorem characterizing the shift-invariant spaces boundedly contained in the Hardy space of square-summable power series to the full Fock space over $\mathbb{C} ^d$. Here, the full Fock space is identified…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
We study nonlinear n-term approximation of harmonic functions on the unit ball in $R^d$ from linear combinations of shifts of the Newtonian kernel (fundamental solution of the Laplace equation) in BMO. A sharp Jackson estimate is…
In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the…
We show a strong maximum principle and an Alexandrov-Bakelman-Pucci estimate for the weak solutions of a Cauchy problem featuring Caputo time-derivatives and non-local operators in space variables given in terms of Bernstein functions of…
Spectral Barron spaces, which quantify the absolute value of weighted Fourier coefficients of a function, have gained considerable attention due to their capability for universal approximation across certain function classes. By…
We derive parametric integral representations for the general $n$-point function of scalar operators in momentum-space conformal field theory. Recently, this was shown to be expressible as a generalised Feynman integral with the topology of…
We present an approximation notion for NP-hard optimization problems represented by binary functions. We prove that (assuming P != NP) the new notion is strictly stronger than FPTAS, but strictly weaker than having a polynomial-time…
We show that inverse problems with a truncated quadratic regularization are NP-hard in general to solve, or even approximate up to an additive error. This stands in contrast to the case corresponding to a finite-dimensional approximation to…
We introduce a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative $\mathrm{L}^p$-space. We equally prove that two classical operator norms, the regular norm and the decomposable norm are…
For weighted Toeplitz operators $\T^N_\phi$ defined on spaces of holomorphic functions in the unit ball, we derive regularity properties of the solutions $f$ to the integral equation $\T^N_\phi(f)=h$ in terms of the regularity of the symbol…
On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…
The $k$-Cauchy-Fueter operators and complexes are quaternionic counterparts of the Cauchy-Riemann operator and the Dolbeault complex in the theory of several complex variables. To develop the function theory of several quaternionic…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
We consider the Schur-Horn problem for normal operators in von Neumann algebras, which is the problem of characterizing the possible diagonal values of a given normal operator based on its spectral data. For normal matrices, this problem is…
In this work, we will present variants Fixed Point Theorem for the affine and classical contexts, as a consequence of general Brouwer's Fixed Point Theorem. For instance, the affine results will allow working on affine balls, which are…
In this paper we investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for $\mu,\lambda\in A_{p,q}$ and $\alpha/n+1/q=1/p$, the norm $\|…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
We consider the sampling problem for two-sided small Fock spaces $\mathcal{F}^p_{\alpha}$, for the full range $0 < p \le \infty$. We establish a geometric description of shift-invariant sampling sequences, i.e., sequences $\Lambda$ such…