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In this paper, having analyzed the previously obtained results devoted to the root vectors series expansion in the Abel-Lidskii sense, we come to the conclusion that the concept can be formulated in the classical terms of the spectral theorem. Though, the spectral theorem for a sectorial operator has not been formulated even in the m-sectorial case, we can consider from this point of view a most simplified case related to the sectorial operator with a discrete spectrum. Thus, in accordance with the terms of the spectral theorem, we naturally arrive at the functional calculus for sectorial operators which is the main focus of this paper. Due to the functional calculus methods, we construct the operator class with the asymptotics more subtle then one of the power type.
The main purpose of this paper is to study cohomology and develop a deformation theory of restricted Lie algebras in positive characteristic $$$p$$$ > $$$0$$$. In the case $$$p\geq3$$$, it is shown that the deformations of restricted Lie algebras are controlled by the restricted cohomology introduced by Evans and Fuchs. Moreover, we introduce a new cohomology that controls the deformations of restricted morphisms of restricted Lie algebras. In the case $$$p=2$$$, we provide a full restricted cohomology complex with values in a restricted module and investigate its connections with formal deformations. Furthermore, we introduce a full deformation cohomology that controls deformations of restricted morphisms of restricted Lie algebras in characteristic $$$2$$$. As example, we discuss restricted cohomology with adjoint coefficients of restricted Heisenberg Lie algebras in characteristic $$$p\geq 2$$$.
In this paper, we study a new class of operators, so called $$$A(n,m)$$$-iso-contra-expansive operators. These new families of operators are considered as a generalization that combines the $$$m$$$-expansive operators as well as m-contractive operators and the classes of $$$(A,m)$$$-expansive and $$$(A,m)$$$-contractive operators and we recover the notion of $$$n$$$-quasi-$$$(A,m)$$$-isometric operators. Some spectral properties of these kind of operators are provided, we derive also a conditions to have the single-valued extension property (SVEP) and we finish by an application of Toeplitz operators on Bergman spaces.
Let $$$G$$$ be a permutation group on a set $$$\Omega$$$ with no fixed points in $$$\Omega$$$, and let $$$m$$$ be a positive integer. If for each subset $$$\Gamma$$$ of $$$\Omega$$$ the size $$$\Gamma^{g}-\Gamma|$$$ is bounded, for $$$g\in G$$$, the movement of $$$g$$$ is defined as move $$$(g):=\max{|\Gamma^{g}-\Gamma|}$$$ over all subsets $$$\Gamma$$$ of $$$\Omega$$$, and move $$$(G)$$$ is defined as the maximum of move $$$(g)$$$ over all non-identity elements of $$$g\in G$$$. Suppose that $$$G$$$ is not a 2-group. It was shown by Praeger that $$$|\Omega|\leqslant\lceil\frac{2mp}{p-1}\rceil+t-1$$$, where $$$t$$$ is the number of $$$G$$$-orbits on $$$\Omega$$$ and $$$p$$$ is the least odd prime dividing $$$|G|$$$. In this paper, we classify all permutation groups with maximum possible degree $$$|\Omega|=\lceil\frac{2mp}{p-1}\rceil+t-1$$$ for $$$t=2$$$, in which every non-identity element has constant movement $$$m$$$.
2025
Volume 25- 16
Numéro 1 (Janvier 2025)2024
Volume 24- 15
Numéro 1 (Janvier 2024)2023
Volume 23- 14
Numéro 1 (Janvier 2023)2022
Volume 22- 13
Numéro 1 (Janvier 2022)2021
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Numéro spécial : AUS-ICMS 20202020
Volume 20- 11
Numéro 1 (Mai 2020)