Related papers: Beurling's Theorem for $SL(2,\R)$

For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof…

the main theorem gives a sufficient condition for a n elements of SL(2,R) to generate a free group.The idea behind it is to use a nonorientable version of the Dehn-Wolpert-Goldman twist and to sew it with the original representation of a…

We construct families of hyperelliptic curves over Q of arbitrary genus g with (at least) g integral elements in K_2. We also verify the Beilinson conjectures about K_2 numerically for several curves with g=2, 3, 4 and 5. The paper is…

Sturm theory for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. Here we propose a Sturm oscillation theorem for indefinite systems of even…

In a previous work we established a super Schur-Weyl-Brauer duality between the orthosymplectic supergroup of superdimension $(m|2n)$ and the Brauer algebra with parameter $m-2n$. This led to a proof of the first fundamental theorem of…

We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is…

We prove a distribution-theoretic conjecture of Robert Coleman, thereby also obtaining an explicit description of the complete set of Euler systems for the multiplicative group over Q.

A proof is given of Rosenthal's \(\ell_1\) theorem.

I propose the group SL(4,R) as a generalisation of the Dirac group SL(2,C) used in quantum mechanics, as a possible basis on which to build a more general theory from which the standard model of particle physics might be derived as an…

We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive…

The famous Burnside-Schur theorem states that every primitive finite permutation group containing a regular cyclic subgroup is either 2-transitive or isomorphic to a subgroup of a 1-dimensional affine group of prime degree. It is known that…

This is a substantial revision of the older version of this paper. The main result of the old version (the equality, up to a factor of 2 of the Beilinson and Borel regulators) is now a conjecture. The main results give equality of Beilinson…

We discuss $SL(2,Z)$ subgroups appropriate for the study of $N=2$ Super Yang-Mills with $N_f=2n$ flavors. Hyperelliptic curves describing such theories should have coefficients that are modular forms of these subgroups. In particular,…

We will prove the Berry-Esseen theorem for the number counting function of the circular $\beta$-ensemble (C$\beta$E), which will imply the central limit theorem for the number of points in arcs of the unit circle in mesoscopic and…

We prove the $P=W$ conjecture for $\mathrm{GL}_n$ for all ranks $n$ and curves of arbitrary genus $g\geq 2$. The proof combines a strong perversity result on tautological classes with the curious Hard Lefschetz theorem of Mellit. For the…

We give a complete description of the representation of $SL(2,\mathbb{C})$ acting in the Hilbert space of the quantum Coulomb field and a constructive consistency proof of the axioms of the quantum theory of the Coulomb field.

G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this…

After Voronin proved the universality theorem of the Riemann zeta function in the 1970s, universality theorems have been proposed for various zeta and L-functions. Drungilas-Garunkstis-Kacenas' work at 2013 on the universality theorem of…

The Brill-Noether Theorem gives necessary and sufficient conditions for the existence of a linear series. Here we consider a general n-fold, etale cyclic cover p of a curve C of genus g and investigate for which numbers r,d a linear series…

In this paper, we generalize the continuous quaternion shearlet transform on $\mathbb{R}^{2}$ to $\mathbb{R}^{2d}$, called the multivariate two sided continuous quaternion shearlet transform. Using the two sided quaternion Fourier…