Related papers: A Refinement of Carlson's Theorem
The $\nu$-zeros of the Bessel functions of purely imaginary order are examined for fixed argument $x>0$. In the case of the modified Bessel function of the second kind $K_{i\nu}(x)$, it is known that it possesses a countably infinite…
This paper is meant to be a gentle introduction to Carleson's Theorem on pointwise convergence of Fourier series.
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…
We prove a Carleman estimate for a one-dimensional parabolic equation which degenerates at one extremity of the domain and has a bounded, time dependent coefficient multiplying the diffusion term. Then we use the estimate to show the null…
We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible.…
The analytical continuation of correlation functions from imaginary to real time is a crucial step in lattice gauge theories, and it challenges our ability to derive non-perturbative predictions from lattice simulations. We review aspects…
We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type…
A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise…
This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincar\'e inequality. Such a functional is defined through relaxation, and it defines a Radon measure on…
In this article, we give two proofs of Carlson's theorem for located words in~$\mathsf{ACA}^+_0$. The first proof is purely combinatorial, in the style of Towsner's proof of Hindman's theorem. The second uses topological dynamics to show…
In this paper we will establish necessary and sufficient conditions for a Laplace-Carleson embedding to be bounded for certain spaces of functions on the positive half-line. We will use these results to characterise weighted (infinite-time)…
Let f be an entire function of finite order less than 1. The maximum modulus M(r) of f and the counting function of the zeros N(r) are connected by a best possible growth inequality known as Valiron's Theorem: For functions subharmonic in…
Conformal theory correlators are characterized by the spectrum and three- point functions of local operators. We present a formula which extracts this data as an analytic function of spin. In analogy with a classic formula due to Froissart…
We give an alternate proof of three versions of the theorem on extrapolation of Carleson measures.
A version of Gabor expansion over a lattice of critical density is shown to converge to an arbitrary function that belongs to domain of the oscillator operator. This expansion is used for approximation of an arbitrary function concentrated…
We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…
Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…
We give a proof of Brooks' theorem and its list coloring extension using the algebraic method of Alon and Tarsi; this also shows that the Brooks' theorem remains valid in a more general game coloring setting.
We extend Krasnoselskii's fixed point result to non-self-real functions. We find a new and simple proof for Hillam's result. In our approach, we don't assume the image of the related mapping to be compact or bounded. In this way, we extend…
Taking the Fourier integral theorem as our starting point, in this paper we focus on natural Monte Carlo and fully nonparametric estimators of multivariate distributions and conditional distribution functions. We do this without the need…