Related papers: Remarks on the Sibony functions and pseudometrics

We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.

We present an effective formula for the Sibony function for all Reinhardt domains.

We introduce the concept of protometric and present some properties of protometrics.

Some results on the discontinuity properties of the Lempert function and the Kobayashi pseudometric in the spectral ball are given.

We discuss continuity and upper semicontinuity of the Wu pseudometric.

We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…

We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…

The parabolic functions are introduced in analogy to the circular and hyperbolic cases. We discuss the relevant properties, the geometrical interpretation and touch on possible generalizations and their link with the modular elliptic…

Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…

We discuss some different results on Sidon-type inequalities and on the space of quasi-continuous functions.

We discuss representations of monogenic functions over very regular groups.

We obtain formulas for the coefficients of positive and negative powers of a partial theta function.

Subaddivity type matrix inequalities for concave funcions and symetric norms are given.

Identities and inequalities for the cosine and sine functions are obtained.

Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…

We give estimates for the squeezing function on strictly pseudoconvex domains, and derive some sharp estimates for the Caratheodory, Sibony and Azukawa metric near their boundaries.

We propose an alternative definition for pseudo-bosons. This simplifies the mathematical structure, minimizing the required assumptions. Some physical examples are discussed, as well as some mathematical results related to the biorthogonal…

We survey the properties of Brody and Kobayashi hyperbolic manifolds.

The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…

We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.