#### Proceedings of the American Mathematical Society

Journal Information

ISSN / EISSN
:
0002-9939 / 1088-6826

Published by: American Mathematical Society (AMS)
(10.1090)

Current Coverage

SCOPUS

Archived in

EBSCO

SHERPA/ROMEO

#### Latest articles in this journal

Published: 24 March 2022

Proceedings of the American Mathematical Society; https://doi.org/10.1090/proc/15905

**Abstract:**

In this work we prove that some integrals of special functions are positive by applying the Plancherel theorem for Hankel transforms and positivity of the modified Bessel functions. We also prove that, except an extra elementary factor, Hankel transforms map subsets of completely monotonic functions into complete monotonic functions.

Published: 24 March 2022

Proceedings of the American Mathematical Society; https://doi.org/10.1090/proc/15882

**Abstract:**

We describe the relations among the $\ell$ -torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent in some sense. Altogether, the three conjectures are equivalent for the class of solvable groups. We then prove the $\ell$ -torsion conjecture for $\ell$ -groups and the other two conjectures for nilpotent groups.

Published: 24 March 2022

Proceedings of the American Mathematical Society; https://doi.org/10.1090/proc/15807

**Abstract:**

Let $M_n$ be drawn uniformly from all $\pm 1$ symmetric $n \times n$ matrices. We show that the probability that $M_n$ is singular is at most $\exp (-c(n\log n)^{1/2})$ , which represents a natural barrier in recent approaches to this problem. In addition to improving on the best-known previous bound of Campos, Mattos, Morris and Morrison of $\exp (-c n^{1/2})$ on the singularity probability, our method is different and considerably simpler: we prove a “rough” inverse Littlewood-Offord theorem by a simple combinatorial iteration.

Published: 24 March 2022

Proceedings of the American Mathematical Society; https://doi.org/10.1090/proc/15951

**Abstract:**

We establish a sharp reciprocity inequality for modulus in compact metric spaces $X$ with finite Hausdorff measure. In particular, when $X$ is also homeomorphic to a planar rectangle, our result answers a question of K. Rajala and M. Romney [Ann. Acad. Sci. Fenn. Math. 44 (2019), pp. 681-692]. More specifically, we obtain a sharp inequality between the modulus of the family of curves connecting two disjoint continua $E$ and $F$ in $X$ and the modulus of the family of surfaces of finite Hausdorff measure that separate $E$ and $F$ . The paper also develops approximation techniques, which may be of independent interest.

Published: 24 March 2022

Proceedings of the American Mathematical Society; https://doi.org/10.1090/proc/15933

**Abstract:**

We show that every finite group $G$ of size at least $3$ has a nilpotent subgroup of class at most $2$ and size at least $|G|^{1/32\log \log |G|}$ . This answers a question of Pyber, and is essentially best possible.

Published: 24 March 2022

Proceedings of the American Mathematical Society; https://doi.org/10.1090/proc/15903

**Abstract:**

It is proven that if $X$ is a Banach space, $K$ and $S$ are locally compact Hausdorff spaces and there exists an $(M, L)$ -quasi isometry $T$ from $C_{0}(K,X)$ onto $C_{0}(S, X)$ , then $K$ and $S$ are homeomorphic whenever $1 \leq M^{2}> S(X)$ , where $S(X)$ denotes the Schäffer constant of $X$ , and $L \geq 0$ . As a consequence, we show that the first nonlinear extension of Banach-Stone theorem for $C_{0}(K, X)$ spaces obtained by Jarosz in 1989 can be extended to infinite-dimensional spaces $X$ , thus reinforcing a 1991 conjecture of Jarosz himself on

Published: 24 March 2022

Proceedings of the American Mathematical Society; https://doi.org/10.1090/proc/15927

**Abstract:**

Quite recently, we have obtained two main theorems dealing with absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series [C. R. Math. Acad. Sci. Paris 359 (2021), pp. 323–328]. In this paper, we have generalized these theorems for a general summability method. We have also obtained some new and known results for certain absolute summability methods.

Published: 24 March 2022

Proceedings of the American Mathematical Society; https://doi.org/10.1090/proc/15843

**Abstract:**

We derive an upper bound for the Assouad dimension of visible parts of self-similar sets generated by iterated function systems with finite rotation groups and satisfying the weak separation condition. The bound is valid for all visible parts and it depends on the direction and the penetrable part of the set, which is a concept defined in this paper. As a corollary, we obtain in the planar case that if the projection is a finite or countable union of intervals then the visible part is 1-dimensional. We also prove that the Assouad dimension of a visible part is strictly smaller than the Hausdorff dimension of the set provided the projection contains interior points. Our proof relies on Furstenberg’s dimension conservation principle for self-similar sets.

Published: 24 March 2022

Proceedings of the American Mathematical Society; https://doi.org/10.1090/proc/15901

**Abstract:**

This paper addresses a subtle issue arising from the measurability of operators with respect to the Dixmier trace.

Published: 24 March 2022

Proceedings of the American Mathematical Society; https://doi.org/10.1090/proc/15871

**Abstract:**

A group $G$ is Jónsson if $|H| > |G|$ whenever $H$ is a proper subgroup of $G$ . Using an embedding theorem of Obraztsov it is shown that there exists a Jónsson group $G$ of infinite cardinality $\kappa$ if and only if there exists a Jónsson algebra of cardinality $\kappa$ . Thus the question as to which cardinals admit a Jónsson group is wholly reduced to the well-studied question of which cardinals are not Jónsson. As a consequence there exist Jónsson groups of arbitrarily large cardinality. Another consequence is that the infinitary edge-orbit conjecture of Babai is true.