Related papers: On Bohr's equivalence theorem
We give a new simpler proof of a theorem of Jayne and Rogers.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.
We prove the reverse ultra log-concavity of the Boros-Moll polynomials. We further establish an inequality which implies the log-concavity of the sequence $\{i!d_i(m)\}$ for any $m\geq 2$, where $d_i(m)$ are the coefficients of the…
In this paper, first we give a new generalization of the Bohr's inequality for the class of bounded analytic functions $\mathcal{B'}$ and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\overline{g},$…
We present a simple proof of Christer Borell's general inequality in the Brunn-Minkowski theory. We then discuss applications of Borell's inequality to the log-Brunn-Minkowski inequality of B\"or\"oczky, Lutwak, Yang and Zhang.
A conjecture of Cigler which realizes normalized q-Hermite polynomials as moments is verified.
In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
Inspired by results of Bayart on ordinary Dirichlet series $\sum a_n n^{-s}$, the main purpose of this article is to start an $\mathcal{H}_p$-theory of general Dirichlet series $\sum a_n e^{-\lambda_{n}s}$. Whereas the…
The converse of Fortin's Lemma in Banach spaces is established in this Note.
We produce twisted derived equivalences between torsors under abelian varieties and their moduli spaces of simple semi-homogeneous sheaves. We also establish the natural converse to this result and show that a large class of twisted derived…
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
In this note we present a simple upper bound for the row-wise norm of the inverses of general confluent Vandermonde matrices.
In this short note, we discuss the Barndorff-Nielsen lemma, which is a generalization of well-known Borel-Cantelli lemma. Although the result stated in the Barndorff-Nielsen lemma is correct, it does not follow from the argument proposed in…
We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the…
A natural occurrence of shift equivalence in a purely algebraic setting constitutes the subject matter of the following short exposition.
We derive some equalities for relations on the algebra A, under the assumption that every subalgebra of A $\times$ A is congruence modular.