Related papers: The extension problem in free harmonic analysis
Using the recent theory of Krein--von Neumann extensions for positive functionals we present several simple criteria to decide whether a given positive functional on the full operator algebra is normal. We also characterize those…
In this paper, we pursue the study of harmonic functions on the real hyperbolic ball started by the second named author. Our focus here is on the theory of Hardy, Hardy-Sobolev and Lipschitz spaces of these functions. We prove here that…
In this work we establish a connection between two classical notions, unrelated so far: Harmonic functions on the one hand and absolutely monotonic functions on the other hand. We use this to prove convexity type and propagation of…
We define the Hardy spaces of free noncommutative functions on the noncommutative polydisc and the noncommutative ball and study their basic properties. Our technique combines the general methods of noncommutative function theory and…
Recently Tomasz Natkaniec in [On lineability of families of non-measurable functions of two variable. Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Mat. RACSAM, 115(1):Paper No. 33, 10, 2021] studied the lineability problem for several…
We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical systems. Under quite general hypotheses, the free energy is shown to be almost upper-semicontinuous: some normalised component of a limit…
We derive a graph expansion for the thermal partition function of solvable two-dimensional models with boundaries. This expansion of the integration measure over the virtual particles winding around the time cycle is obtained with the help…
We survey results from amenability theory with an emphasis on applications to harmonic analysis on direct-limit groups.
Given a function $f : A \to \mathbb{R}^n$ of a certain regularity defined on some open subset $A \subseteq \mathbb{R}^m$, it is a classical problem of analysis to investigate whether the function can be extended to all of $\mathbb{R}^m$ in…
In this paper we introduce some new methods to understand the analytic behaviour of the zeta function of a group. We can then combine this knowledge with suitable Tauberian theorems to deduce results about the growth of subgroups in a…
This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical…
This is a continuation of our previous work in bi-free harmonic analysis for commuting left and right variables. Here we analyze the bi-free partial S-transform and use the results to study limit theorems and infinite divisibility relative…
We construct a free group of continuum many generators among those autobijections of $\mathbb{R}$ which are also Hamel bases of $\mathbb{R}^2$, with identity function included. We also observe two new cases when a real function is a…
With view to applications, we establish a correspondence between two problems: (i) the problem of finding continuous positive definite extensions of functions $F$ which are defined on open bounded domains $\Omega$ in $\mathbb{R}$, on the…
Refining a constructive combinatorial method due to MacLane and Schilling, we give several criteria for a valued field that guarantee that all of its maximal immediate extensions have infinite transcendence degree. If the value group of the…
We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.
The residual finiteness growth of a group quantifies how well approximated the group is by its finite quotients. In this paper, we construct groups with arbitrarily large residual finiteness growth. We also demonstrate a new relationship…
Factors $\frac{X}{Y}$ in a free group $F$ with $Y$ normal in $X$ are considered. Precise results on the free structure of ${Y}$ relative to the free structure of ${X}$ when $\frac{X}{Y}$ is abelian are obtained. Some extensions and…
The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and…
We prove some uniqueness results for positive harmonic functions on the unit ball satisfying a nonlinear boundary condition