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In the present paper, we study the shifted hypergeometric function f(z)=z_{2}F_{1}(a,b;c;z) for real parameters with 0

Mean dimension may decrease after taking the natural extension. In this paper we show that mean dimension is preserved by natural extension for an endomorphism on a compact metrizable abelian group. As an application, we obtain that the mean dimension of an algebraic cellular automaton coincides with the mean dimension of its natural extension, which strengthens a result of Burguet and Shi [Israel J. Math. (to appear).] with a different proof. [ABSTRACT FROM AUTHOR]

The heat semigroup on discrete hypercubes is well-known to be contractive over L_p-spaces for 1

We provide an elementary proof of a result by V. P. Fonf and C. Zanco on point-finite coverings of separable Hilbert spaces. Indeed, by using a variation of the famous argument introduced by J. Lindenstrauss and R. R. Phelps [Israel J. Math. 6 (1968), pp. 39–48] to prove that the unit ball of a reflexive infinite-dimensional Banach space has uncountably many extreme points, we prove the following result. Let X be an infinite-dimensional Hilbert space satisfying dens(X)< 2ℵ0, then X does not admit point-finite coverings by open or closed balls, each of positive radius. In the second part of the paper, we follow the argument introduced by V. P. Fonf, M. Levin, and C. Zanco in [J. Geom. Anal. 24 (2014), pp. 1891–1897] to prove that the previous result holds also in infinite-dimensional Banach spaces that are both uniformly rotund and uniformly smooth. [ABSTRACT FROM AUTHOR]

We prove that the ideal of nowhere Ramsey sets is Tukey reducible to each of the finite-dimensional Silver null ideals. This is in line with an earlier result of the author [Israel J. Math. 211 (2016), pp. 473–480] that the meager ideal is Tukey reducible to the Silver null ideal, and it answers two questions asked by Spinas and Wohofsky [Fund. Math. 254 (2021), pp. 261–303]. We also show that if the homogeneity number \mathfrak {hm} equals 2^{\aleph _0}, then the additivity of the Marczewski ideal is below the \sigma-splitting number \mathfrak {s_\sigma }. [ABSTRACT FROM AUTHOR]

We improve bump conditions for the two-weight boundedness of Calderón-Zygmund operators introduced recently by R. Rahm and S. Spencer [Israel J. Math. 223 (2018), pp. 197–204]. [ABSTRACT FROM AUTHOR]

Any coded subshift XC defined by a set C of code words contains a subshift, which we call LC, consisting of limits of single code words. We show that when C satisfies the unique decipherability property, the topological entropy h(XC) of XC is determined completely by h(LC) and the number of code words of each length. More specifically, we show that h(XC) = h(LC) exactly when a certain infinite series is less than or equal to 1, and when that series is greater than 1, we give a formula for h(XC). In the latter case, an immediate corollary (using a result from [Israel J. Math. 192 (2012), pp. 785-817] is that XC has a unique measure of maximal entropy. [ABSTRACT FROM AUTHOR]