Article
Mathematics, Applied
P. Muthukumar, Ajay K. Sharma, Vivek Kumar
Summary: This paper introduces a discrete analogue of weighted Hardy spaces on rooted trees and extensively investigates the weighted composition operators between them. In particular, the bounded and compact weighted composition operators between discrete Hardy spaces are characterized.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
P. Muthukumar, P. Shankar
Summary: Muthukumar and Ponnusamy [9] studied multiplication operators on T-p spaces. In this article, we mainly consider multiplication operators between T-p and T-q (p ? q). We characterize bounded and compact multiplication operators from T-p to T-q, and prove that there are no invertible multiplication operators and isometric multiplication operators from T-p to T-q for p ? q. Additionally, we discuss fixed points of a multiplication operator on T-p.
LOBACHEVSKII JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Federico Santagati
Summary: We study a homogeneous tree with an exponential growth nondoubling flow measure mu and a self-adjoint probabilistic Laplacian L with respect to mu. We prove that the maximal characterization based on the heat and Poisson semigroups of L, as well as the Riesz transform characterization of the atomic Hardy space introduced in a previous work, fail.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics
Laura Arditti, Anita Tabacco, Maria Vallarino
Summary: The paper introduces a BMO space for metric measure spaces, proving its relationship with a Hardy space and investigating the sharp maximal function associated with BMO space.
JOURNAL OF GEOMETRIC ANALYSIS
(2021)
Article
Mathematics
M. H. Khalifeh, Abdol-Hossein Esfahanian
Summary: This passage discusses the problem of finding the minimum weight sum in a vertex and edge weighted graph G. It introduces the concept of best switch (BS) and defines three notions: convexity, discrete derivative, and discrete integral for VEW graphs. An algorithm is also proposed to solve the BS problem for positively VEW trees.
Article
Mathematics, Applied
Charles Fefferman, Bo'az Klartag
Summary: This paper studies the extension problem of a function defined on the leaves of a weighted tree, aiming to find an appropriate extension function F by minimizing the weighted W-1,W-p-Sobolev norm of the extension. The harmonic extension operator can satisfy the requirements when p=2. However, in the case of a radially symmetric binary tree, neither the averaging operator nor the harmonic extension operator is applicable. Nevertheless, we prove the existence of a linear extension operator whose norm is bounded by a constant depending solely on p. This operator is a variant of the standard harmonic extension operator and is harmonic extension with respect to a certain Markov kernel determined by p and the weights.
ADVANCED NONLINEAR STUDIES
(2023)
Article
Mathematics, Applied
Shyam Swarup Mondal
Summary: In this article, we present symbolic criteria for the boundedness of pseudo differential operators on the homogeneous tree X. We also provide a sufficient condition for weak type (p, q) boundedness. Additionally, we give necessary and sufficient conditions on the symbols sigma such that the corresponding pseudo-differential operators T-sigma from L-p1 (X) into L-p2 (X) are nuclear for 1 <= p(1), p(2) < infinity. Furthermore, explicit formulas for the symbol of the adjoint and product of the nuclear pseudo differential operators on X are provided.
ANALYSIS AND MATHEMATICAL PHYSICS
(2022)
Article
Mathematics
Yi Zhang, Xiaosong Peng, Yuanyuan Zhang
Summary: In this paper, the concept of an omega-dendriform algebra is introduced and the relationship between omega-Rota-Baxter algebras and omega-dendriform algebras is shown. A multiplication recursion definition of typed, angularly decorated rooted trees is provided, and the free omega-Rota-Baxter algebra is constructed using typed, angularly decorated rooted trees.
Article
Mathematics, Applied
V. V. Favaro, P. Hai, D. M. Pellegrino, O. R. Severiano
Summary: The research investigates composition operators C-Phi on the Hardy-Smirnov space H-2(Omega) induced by analytic self-maps Phi of an open simply connected proper subset Omega of the complex plane. New proofs for adjoint formulas and descriptions of certain composition operators on H-2(Omega) are provided.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Toru Kajigaya
Summary: This article investigates the stabilities of weighted length or energy functional of a discrete map and proves the non-existence of stable discrete minimal immersion or non-constant stable discrete harmonic map in certain homogeneous spaces.
ANNALI DI MATEMATICA PURA ED APPLICATA
(2023)
Article
Mathematics
Tapendu Rana, Sumit Kumar Rano
Summary: The aim of this article is to investigate the L'-boundedness of pseudo-differential operators on a homogeneous tree X. We establish a connection between the L'-boundedness of these operators on X and that on the group of integers Z for p is an element of (1, 2). In addition, we prove a counterpart of Calderon-Vaillancourt theorem for p is an element of (1, infinity) \ {2} in the setting of homogeneous trees.
STUDIA MATHEMATICA
(2023)
Article
Mathematics, Applied
Lorenzo Ciardo
Summary: The study compares the Perron value and moment of a rooted tree T, showing that mu(T) is almost an upper bound for rho(T) and the ratio mu(T)/rho(T) is unbounded but at most linear in the order of T. Additionally, two new objects associated with T - the Perron entropy and the neckbottle matrix are introduced and the impact of different operations on the set of rooted trees on the Perron value and moment is investigated.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2022)
Article
Mathematics, Applied
The Anh Bui, The Quan Bui, Qing Hong, Guorong Hu
Summary: This paper focuses on the study of non-negative self-adjoint operators and their heat kernels on Ahlfors n-regular metric measure spaces. By using spectral theory, the imaginary power operator is defined and a certain estimate is proved for the kernel of spectral multiplier operators under certain conditions. The results apply to stratified Lie groups and Hermite operators on R-n with a certain dimension.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics
Ryutaro Arai, Eiichi Nakai, Yoshihiro Sawano
Summary: The generalized fractional integral operators are proven to be bounded from one Orlicz-Hardy space to another, extending the previous result proved by Stein and Weiss in 1960.
MATHEMATISCHE NACHRICHTEN
(2021)
Article
Mathematics, Applied
Weichao Guo, Jianmiao Ruan, Guoping Zhao
Summary: This study demonstrates that the Hilbert Hausdorff operator H-Φ is unbounded in a variety of quasi-Banach spaces, unless it is a zero operator.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics
Perumal Muthukumar, Saminathan Ponnusamy
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2017)
Article
Mathematics, Applied
Perumal Muthukumar, Saminathan Ponnusamy
ANALYSIS AND MATHEMATICAL PHYSICS
(2017)
Article
Mathematics
Perumal Muthukumar, Saminathan Ponnusamy, Herve Queffelec
INTEGRAL EQUATIONS AND OPERATOR THEORY
(2018)
Article
Mathematics
Perumal Muthukumar, Saminathan Ponnusamy
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
(2018)
Article
Mathematics
P. Muthukumar, Jaydeb Sarkar
Summary: This paper studies model spaces that are invariant under composition operators, with emphasis on finite-dimensional model spaces, affine transformations, and linear fractional transformations.
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
(2022)
Article
Mathematics, Applied
P. Muthukumar, Ajay K. Sharma, Vivek Kumar
Summary: This paper introduces a discrete analogue of weighted Hardy spaces on rooted trees and extensively investigates the weighted composition operators between them. In particular, the bounded and compact weighted composition operators between discrete Hardy spaces are characterized.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Snehasish Bose, P. Muthukumar, Jaydeb Sarkar
Summary: The paper aims to characterize invariant subspaces of composition operators and study the properties and applications of inner functions theta.
JOURNAL OF OPERATOR THEORY
(2021)
