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If a differential equation in a Banach manifold is invariant or quasi-invariant under the action of one or more Lie groups, then its stationary points cannot be isolated, so that classical linearized stability theorem does not apply to it.…
In this paper we define Banach spaces of overconvergent half-integral weight $p$-adic modular forms and Banach modules of families of overconvergent half-integral weight $p$-adic modular forms over admissible open subsets of weight space.…
Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces, random normed modules and random locally convex modules.…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
The primary objective of this paper is to develop methodologies for investigating Schwarz type lemmas and to present their applications in Banach spaces. First, we improve upon the main results obtained by Osserman [Proc. Am. Math. Soc.…
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For a compact negatively curved space, we develop a thermodynamic formalism framework to study the space of quasimorphisms of its fundamental group modulo bounded functions. We prove that this space is Banach isomorphic to the space of…
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We provide a sharp monotonicity theorem about the distribution of subharmonic functions on manifolds, which can be regarded as a new, measure theoretic form of the uncertainty principle. As an illustration of the scope of this result, we…
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This paper studies approximation properties of linear sampling operators in general Banach lattices $X$. We obtain matching direct and inverse approximation estimates, convergence criteria, equivalence results involving special…
We prove the existence of measurable invariant manifolds for small perturbations of linear Random Dynamical Systems evolving on a Banach space and admitting a general type of dichotomy, both for continuous and discrete time. Moreover, the…
The basic results for nonlinear operators are given. These results include nonlinear versions of classical uniform boundedness theorem and Hahn-Banach theorem. Furthermore, the mappings from a metrizable space into another normed space can…
In this work, a new concept of nonself total asymptotically nonexpansive mapping is introduced and an iterative process is considered for two nonself totally asymptotically nonexpansive mappings. Weak and strong convergence theorems for…
This work is motivated by a question published in E. Glasner's paper On a question of Kazhdan and Yom Din regarding the possibility to approximate functionals on a Banach space which are almost invariant with respect to an action of a…
The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch…