Zobrazeno 1 - 10
of 271
pro vyhledávání: '"26A12"'
Autor:
Hilberdink, Titus
In this paper we develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations. For example, $n+2\to 2n\to 2^n\to 2^{\cdot^
Externí odkaz:
http://arxiv.org/abs/2409.06661
Autor:
Polasek, Iván, Rela, Ezequiel
In this article we study the generalized Fourier dimension of the set of Liouville numbers $\mathbb{L}$. Being a set of zero Hausdorff dimension, the analysis has to be done at the level of functions with a slow decay at infinity acting as control fo
Externí odkaz:
http://arxiv.org/abs/2408.04148
Autor:
Elliott, Jesse
This monograph elucidates and extends many theorems and conjectures in analytic number theory and algebraic asymptotic analysis via the natural notions of degree and logexponential degree. The Riemann hypothesis, for example, is equivalent to the sta
Externí odkaz:
http://arxiv.org/abs/2407.17820
Autor:
Baraniewicz, Miłosz
We give two-sided estimates of a ground state for Schr\"odinger operators with confining potentials. We propose a semigroup approach, based on resolvent and the Feynman--Kac formula, which leads to a new, rather short and direct proof. Our results ta
Externí odkaz:
http://arxiv.org/abs/2407.09267
We study the number of indecomposable summands in tensor powers of the vector representation of SL2. Our main focus is on positive characteristic where this sequence of numbers and its generating function show fractal behavior akin to Mahler function
Externí odkaz:
http://arxiv.org/abs/2405.16786
This paper is a short overview of the main Abelian- and Tauberian-type results from [4, 14, 26] regarding the asymptotic analysis of different classes of generalized functions in terms of appropriate frames. The Tauberian-type results provide a compr
Externí odkaz:
http://arxiv.org/abs/2404.04468
In the proof of the classical Borel lemma [6] given by Hayman [11], any positive increasing continuous function $T(r)$ satisfies $T\Big(r+\frac{1}{T(r)}\Big)<2T(r)$ outside a possible exceptional set of linear measure $2$. This result is pivotal in t
Externí odkaz:
http://arxiv.org/abs/2401.14481
Autor:
Schindl, Gerhard
Publikováno v:
J. Math. Anal. Appl. 541, no. 1, 128682, 2025
We answer a question from A. V. Abanin and P. T. Tien about so-called almost subadditive weight functions in the sense of Braun-Meise-Taylor. Using recent knowledge of a growth index for functions, crucially appearing in the ultraholomorphic setting,
Externí odkaz:
http://arxiv.org/abs/2401.10933
Autor:
Horst, Ulrich, Xu, Wei
This paper provides and extends second-order versions of several fundamental theorems on first-order regularly varying functions such as Karamata's theorem/representation and Tauberian's theorem. Our results are used to establish second-order approxi
Externí odkaz:
http://arxiv.org/abs/2311.02655
We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix. In this way we transfer and extend known results from J. Siddiqi and M
Externí odkaz:
http://arxiv.org/abs/2307.14762