Related papers: The `Real' Schwarz Lemma
The purpose of this book is to provide an introduction to one of the fundamental tools of abstract harmonic analysis, namely the Selberg trace formula.
This note contains a short proof of the functional equation for the zeta function.
The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
In this paper we obtain some new Schwarz related inequalities in inner product spaces over the real or complex number field. Applications for the generalized triangle inequality are also given.
In the context of extriangulated categories, we establish the injective version of Schanuel's lemma in homological algebra.
This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.
In this paper we give some applications of a lemma of Babalola and Opoola \cite{BO}, which is a classical extension of an earlier one by Lewandowski, Miller and Zlotkiewicz \cite{LMZ}. The applications were given via a new generalization of…
The purpose of this paper is to study the properties of the solutions to the biharmonic equations: $\Delta(\Delta f)=g$, where $g:$ $\overline{\mathbb{D}}\rightarrow\mathbb{C}$ is a continuous function and $\overline{\mathbb{D}}$ denotes…
Given any polynomial with real coefficients, the existence of a real quadratic polynomial factor is proven using only basic real analysis. The aim is to provide an approachable proof to anybody who is familiar with the least upper bound…
This survey is a guide for the non specialist on how to use rational homotopy theory techniques to get approximations of Farber's topological complexity, in particular, and of Schwarz's sectional category, in general.
We present drawings on the complex plane of the lines Im(zeta(s))=0 and Re(zeta(s))=0. This allow to illustrate many properties of the zeta function of Riemann. This is an expository paper. It does not pretend to prove any new result about…
In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.
For any positive invertible matrix $A$ and any normal matrix $B$ in $M_{n}({\Bbb C})$, we investigate whether the inequality $ ||A\sharp (B^{*}A^{-1}B)||\geq ||B|| $ is true or not, where $\sharp$ denotes the geometric mean and $||\cdot||$…
For a given continuous function $g:~\Omega\rightarrow\mathbb{C}$, we establish some Schwarz type Lemmas for mappings $f$ in $\Omega$ satisfying the {\rm PDE}: $\Delta f=g$, where $\Omega$ is a subset of the complex plane $\mathbb{C}$. Then…
We proove a Bloch's theorem in an almost complex projective plane.
We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.
In this note we investigate connections between zero density estimates for the Riemann zeta function and large value estimates for Dirichlet polynomials. It is well known that estimates of the latter type imply estimates of the former type.…
In this short note, we briefly discuss the Borel-Cantelli lemma and propose a new generalization of the first part of it.
The purpose of this survey is to give a comprehensive introduction to some classes of classical and recent analytic inequalities in Inner Product Spaces.