Related papers: Remarks on the Sibony functions and pseudometrics
This article establishes several remarkably simple identities relating certain metric invariants of level curves of real and complex functions. In particular, we relate lengths of level curves to their curvature and to the gradient field of…
We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at $-\infty$, and uniform hyperbolic bounds are derived. The same questions are addressed for the…
A description of eigensubspaces of the cosine and sine operators is presented. The spectrum of each of these two operator consists of two eigenvalues (1,\,-1) and their eigensubspaces are infinite--dimensional. There are many possible bases…
A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.
In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions.
Antonymous functions are real-valued functions on the Stone spectrum of a von Neumann algebra R. They correspond to the self-adjoint operators in R, which are interpreted as observables in quantum physics. Antonymous functions turn out to…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
We discuss several classical and recent proofs of the isoperimetric inequality and the Sobolev inequality.
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
Let $\Omega$ be a strongly pseudoconvex domain. We introduce the Mabuchi space of strongly plurisubharmonic functions in $\Omega$. We study metric properties of this space using Mabuchi geodesics and establish regularity properties of the…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
The authors provide a survey of certain aspects of their joint work with the late M. K. Vamanamurthy. Most of the results are simple to state and deal with special functions, a topic of research where S. Ramanujan's contributions are…
In this paper, we study several degenerate trigonometric functions, which are degenerate versions of the ordinary trigonometric functions, and derive some identities among such functions by using elementary methods. Especially, we obtain…
We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in $\mathrm{PO}(n,1)$ with $n>3$. We further show that under an additional assumption (satisfied in all known cases), the covolumes of these…
We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold $(M,J)$ admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the…
These notes are intended to provide an introduction to supersymmetry. The notes begin with supersymmetric quantum mechanics and the basic properties of spinor fields. The supersymmetry of simple theories of spin-zero and spin-one-half…
We discuss some differences in the properties of both even and odd Fedosov and Riemannian supermanifolds.