Related papers: A note on Tauberian Theorems of Exponential Type

A structure theorem is proved for strongly holonomic modules over a quantum torus (a crossed product of a field with a free abelian group in which the field is central). This can be applied to give a structure theorem for finitely presented…

We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem,…

We give a proof and extension of two formulas of Frobenius and Stickelberger of Differential Calculus that they used in a fundamental paper concerning elliptic functions theory. Our main ingredient is the introduction of a bilinear form…

Clozel, Harris, and Taylor proposed a conjectural generalized Ihara's lemma for definite unitary groups. In this paper, we prove their conjecture with banal coefficients under some conditions. As an application, we prove a level-raising…

We give an analog of Frobenius' theorem about the factorization of the group determinant on the group algebra of finite abelian groups and we extend it into dihedral groups and generalized quaternion groups. Furthermore, we describe the…

Recently, Buan and Marsh showed that if two complete $\tau$-exceptional sequences agree in all but at most one term, then they must agree everywhere, provided the algebra is $\tau$-tilting finite. They conjectured that the result holds…

The paper introduces in a new although maybe unusual form the examples of types provided by J. von Neumann and F.J. Murray in their outstanding papers on algebraic factorization (1936-1943)pursuing three main aims: speculating about the…

In this article we will introduce a central problem in additive combinatorics, which arised from the famous van der Waerden theorem and an early conjecture of Erd\H{o}s and Tur\'{a}n. The first important theorem was due to Roth in 1953.…

Recently the new q-Euler numbers are defined. In this paper we derive the the Kummer type congruence related to q-Euler numbers and we introduce some interesting formulae related to these q-Euler numbers.

It is shown that the Baer-Kaplansky theorem can be extended to all abelian groups provided that the rings of endomorphisms of groups are replaced by trusses of endomorphisms of corresponding heaps. That is, every abelian group is determined…

We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…

A representation theory of the quantized Poincar\'e ($\kappa$-Poincar\'e) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the non-deformed Poincar\'e algebra. A…

Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…

This paper extends two recent improvements in the Hilbert space setting of the well-known Katznelson-Tzafriri theorem by establishing both a version of the result valid for bounded representations of a large class of abelian semigroups and…

We give a proof of the cyclicity conjecture of Akasaka-Kashiwara, for simply laced types, via quiver varieties. We get also an algebraic characterization of the standard modules.

Tangent spaces to Schubert varieties of type A were characterized by Lakshmibai and Seshadri. This result was extended to the other classical types by Lakshmibai. We give a uniform characterization of tangent spaces to Schubert varieties in…

We present short proofs of Toru\'nczyk's well-known characterization theorems of the Hilbert cube and Hilbert space, respectively.

This paper proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the…

In a previous paper, we showed that profinite $L$-algebras (where $L$ is a variety of modal algebras generated by its finite members) are monadic over $\mathbf{Set}$. This monadicity result suggests that profinite $L$-algebras could be…

Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky's univalence axiom. This makes many extensionality principles, like function and propositional extensionality, directly…