Related papers: Regularity properties of the $\alpha$-Wilton funct…
We study the regularity of exceptional actions of groups by $C^{1,\alpha}$ diffeomorphisms on the circle, i.e. ones which admit exceptional minimal sets, and whose elements have first derivatives that are continuous with concave modulus of…
Fix irrational numbers $\alpha,\hat\alpha>1$ of finite type and real numbers $\beta,\hat\beta\ge 0$, and let $B$ and $\hat B$ be the Beatty sequences $$ B:=(\lfloor\alpha m+\beta\rfloor)_{m\ge 1}\quad\text{and}\quad\hat…
In a previous paper, we showed the existence of an uncountable set of points on the unit circle at which the Rogers-Ramanujan continued fraction does not converge to a finite value. In this present paper, we generalise this result to a…
The Mittag-Leffler function $E_{\alpha}$ being a natural generalization of the exponential function, an infinite-dimensional version of the fractional Poisson measure would have a characteristic functional \[ C_{\alpha}(\phi)…
The function $\Gamma$ on the space of graphons, introduced in [CGH$^+$15], aims to measure the extent to which a graphon $w$ exhibits the Robinson property: for all $x<y<z$, $w(x,z)\leq \min\{ w(x,y),w(y,z)\}$. Robinson graphons form a…
We prove special cases of the Ratios Conjecture for the family of quadratic Dirichlet $L$--functions over function fields. More specifically, we study the average of $L(1/2+\alpha,\chi_D)/L(1/2+\beta,\chi_D)$, when $D$ varies over monic,…
We study traces of a class of subharmonic functions to Ahlfors regular subsets of $\Co^{n}$. In particular, we establish for the traces a generalized BMO-property and the reverse H\"{o}lder inequality.
We give a characterization of $BMO^\alpha$-martingale spaces by using fractional Carleson measures. We get the boudedness of martingale transform and square function on $BMO^\alpha$-martingale spaces easily by using this characterization.…
We prove a structure theorem for stable functions on amenable groups, which extends the arithmetic regularity lemma for stable subsets of finite groups. Given a group $G$, a function $f\colon G\to [-1,1]$ is called stable if the binary…
We study the regularity of solutions of elliptic fractional systems of order 2s, $s \in (0, 1)$, where the right hand side f depends on a nonlocal gradient and has the same scaling properties as the nonlocal operator. Under some structural…
The Gell-Mann -- Low function \beta(g) in QED (g is the fine structure constant) is reconstructed. At large g, it behaves as \beta_\infty g^\alpha with \alpha\approx 1, \beta_\infty\approx 1.
We study new $1/24$ BPS circular Wilson loops in ABJ(M) theory, which are defined in terms of several parameters that continuously interpolate between previously known $1/6$ BPS loops (both bosonic and fermionic) and $1/2$ BPS fermionic…
We present a thorough observational investigation of the heuristic quantised ringdown model presented in Foit & Kleban (2019). This model is based on the Bekenstein-Mukhanov conjecture, stating that the area of a black hole horizon is an…
We introduce a new two-parameter fractional time operator with Volterra structure, denoted by the W-operator, defined through a generalized Laplace symbol. The operator preserves the Caputo-type high-frequency behavior while allowing a…
We consider special flows over the rotation on the circle by an irrational $\alpha$ under roof functions of bounded variation. The roof functions, in the Lebesgue decomposition, are assumed to have a continuous singular part coming from a…
We consider regularity for solutions of a class of de Rham's functional equations. Under some smoothness conditions of functions consisting the equation, we improve some results in Hata (Japan J. Appl. Math. 1985). Our results are…
We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl -Titchmarsh…
The study of the Mittag-Leffler function and its various generalizations has become a very popular topic in mathematics and its applications. In the present paper we prove the following estimate for the $q$-Mittag-Leffler function:…
We investigate the algebraic genericity of various families of continuous functions exhibiting extreme irregularity, focusing on fractal dimensions, H\"older regularity, and fractional differentiability. Our first main result shows that for…
We study the regularity properties of random wavelet series constructed by multiplying the coefficients of a deterministic wavelet series with unbounded I.I.D. random variables. In particular, we show that, at the opposite to what happens…