Related papers: Representative functions of maximal monotone opera…
We provide a characterization for maximal monotone realizations for a certain class of (nonlinear) operators in terms of their corresponding boundary data spaces. The operators under consideration naturally arise in the study of…
Let $k\ge 2$ be an integer and let $A$ be a set of nonnegative integers. The representation function $R_{A,k}(n)$ for the set $A$ is the number of representations of a nonnegative integer $n$ as the sum of $k$ terms from $A$. Let $A(n)$…
The concept of rotation symmetric functions from the Boolean domain is extended to the multiple-valued (MV) domain. It is shown that symmetric functions are a subset of the rotation symmetric functions. Functions exhibiting these kinds of…
Maximal angular operator sends a function defined in a sector of the complex plane to a Maximal angular operator sends a function defined in a sector of the complex plane with vertex at 0 to the function of modulus obtained by maximizing…
A cornerstone in convex analysis is the crucial relationship between functions and their convex conjugate via the Fenchel-Young inequality. In this dual variable setting, the maximal monotonicity of the contact set $ \big\{(x,y) \ \big| \…
This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…
In this paper a theory of Hecke operators for higher order modular forms is established. The definition of cusp forms and attached L-functions is extended beyond the realm of parabolic invariants. The role of representation theoretic…
Let $ N \in \mathbb{N} $, $ N \geq 2 $, be given. Motivated by wavelet analysis, we consider a class of normal representations of the $ C^* $-algebra $ \mathfrak{A}_{N} $ on two unitary generators $ U $, $ V $ subject to the relation \[…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
The modular representation theory of finite groups has its origins in the work of Richard Brauer. In this survey article we first discuss the work being done on some outstanding conjectures in the theory. We then describe work done in the…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the…
The Majorana representation of spin operators allows for efficient field-theoretical description of spin-spin correlation functions. Any N-point spin correlation function is equivalent to a 2N-point correlator of Majorana fermions. For a…
The Hardy-Littlewood maximal function $\mathcal{M}$ and the trigonometric function $\sin{x}$ are two central objects in harmonic analysis. We prove that $\mathcal{M}$ characterizes $\sin{x}$ in the following way: let $f \in…
On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Amp\`ere operator is defined. It is shown that it satisfies a…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
We study the connection between cyclic quasi-monotonicity and quasi-convexity, focusing on whether every cyclically quasi-monotone (possibly multivalued) map is included in the normal cone operator of a quasi-convex function, in analogy…
The differential equations for a continuous birepresentation of a local analytic Moufang loop are established. The commutation relations for the infinitesimal operators of the representation are found. These commutation relations can be…
The notion of derivatives for smooth representations of $GL(n,\mathbb{Q}_p)$ was defined in [BZ77]. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations in [Sah89] and called the…