Related papers: A Frobenius-type theorem for singular Lipschitz di…

This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.

By showing the compatibility of folding almost positive roots and folding cluster categories, we prove that there is a one-to-one correspondence between seeds and tilting seeds in non-simply-laced finite cases.

We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sum of derivatives of generalized lattice…

The aim of this article is to obtain variations on the classical theorems of Schur and Baer on finiteness of commutator subgroups, valid in the contexts of Lie algebras and Leibniz algebras over a field. Using non-abelian tensor products…

Given a singular foliation satisfying locally everywhere the Frobenius condition, even at the singularities, we show how to construct its global sheaves of jets. Our construction is purely formal, and thus applicable in a variety of…

We give a short proof of a Grothendieck-Lefschetz Theorem for equivariant Picard groups of nonsingular varieties with the action of an affine algebraic group.

The classical McShane-Whitney extension theorem for Lipschitz functions is refined by showing that for a closed subset of the domain, it remains valid for any interval of the real line. This result is also extended to the setting of locally…

We consider a new class $\boldsymbol{Q}$ of distribution functions $F$ that have the property of rational-infinite divisibility: there exist some infinitely divisible distribution functions $F_1$ and $F_2$ such that $F_1=F*F_2$. A…

We consider random walks on semisimple Lie groups where the support of the step distribution generates (as a group) a Zariski dense discrete subgroup of infinite covolume. When the semisimple Lie group has property (T), we show that the…

We develop an approach analogous to classical Frobenius theory for the analysis of singularities of ODEs in the case of discrete dynamical systems. Our methodology is based on the Roman-Rota theory of finite operators and relies crucially…

We prove that supports of a wide class of temperate distributions with uniformly discrete support and spectrum on Euclidean spaces are finite unions of translations of full-rank lattices. This result is a generalization of the corresponding…

We develop theory and examples of monoidal functors on tensor categories in positive characteristic that generalise the Frobenius functor from \cite{Os, EOf, Tann}. The latter has proved to be a powerful tool in the ongoing classification…

A recently proposed criterion for the existence of local quantum fields with a prescribed factorizing scattering matrix is verified in a non-trivial model, thereby establishing a new constructive approach to quantum field theory in a…

In this paper we present a combinatorial proof of the Kronecker--Weber Theorem for global fields of positive characteristic. The main tools are the use of Witt vectors and their arithmetic developed by H. L. Schmid. The key result is to…

We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyans theorem.

Suppose that R is a two-dimensional normal standard-graded domain over a finite field. We prove that there exists a uniform Frobenius test exponent b for the class of homogeneous ideals in R generated by at most n elements. This means that…

This paper provides a realization of all classical and most exceptional finite groups of Lie type as Galois groups over function fields over F_q and derives explicit additive polynomials for the extensions. Our unified approach is based on…

We introduce continuous Frobenius categories. These are topological categories which are constructed using representations of the circle over a discrete valuation ring. We show that they are Krull-Schmidt with one indecomposable object for…

We provide precise formulations and proofs of two theorems from Darboux's lectures on orthogonal systems. These results provide local existence and uniqueness of solutions to certain types of first order PDE systems where each equation…

We give a proof of Gabber's presentation lemma for finite fields. We use ideas from Poonen's proof of Bertini's theorem to prove this lemma in the special case of open subsets of the affine plane. We then reduce the case of general smooth…