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Rota-Baxter operators on various structures have found important applications in diverse areas, from renormalization of quantum field theory to Yang-Baxter equations. Relative Rota-Baxter operators on Lie algebras are closely related to pre-Lie algeb
Externí odkaz:
http://arxiv.org/abs/2408.06096
Rota-Baxter groups with weights $\pm 1$ have attracted quite much attention since their recent introduction, thanks to their connections with Rota-Baxter Lie algebras, factorizations of Lie groups, post- and pre-Lie algebras, braces and set-theoretic
Externí odkaz:
http://arxiv.org/abs/2405.11288
Autor:
Kainen, Paul C., Vogt, A.
Publikováno v:
{\it Handbook on Neural Information Processing}, Monica Bianchini, Marco Maggini, Lakhmi C. Jain, Eds., Springer, ISRL Vol. 49, 2013, Chap. 6, pp. 183--214
A Bochner integral formula is derived that represents a function in terms of weights and a parametrized family of functions. Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are established, var
Externí odkaz:
http://arxiv.org/abs/2302.13228
For $0<\nu_2<\nu_1\leq 1$, we analyze a linear integro-differential equation on the space-time cylinder $\Omega\times(0,T)$ in the unknown $u=u(x,t)$ $$\mathbf{D}_{t}^{\nu_1}(\varrho_{1}u)-\mathbf{D}_{t}^{\nu_2}(\varrho_2 u)-\mathcal{L}_{1}u-\mathcal
Externí odkaz:
http://arxiv.org/abs/2210.05009
Autor:
Zhu Jianbo, Yan Dongxue
Publikováno v:
Demonstratio Mathematica, Vol 57, Iss 1, Pp 399-430 (2024)
In this article, we investigate the existence and regularity of solutions for non-autonomous integrodifferential evolution equations involving nonlocal conditions. Using the theory of resolvent operators, some fixed point theorems, and an estimation
Externí odkaz:
https://doaj.org/article/e6db12ddff2c48d586cb88aaf2c8fa13
Autor:
Król, Sebastian
We provide a convenient framework for the study of the well-posedness of a variety of abstract (integro)differential equations in general Banach function spaces. It allows us to extend and complement the known theory on the maximal regularity of such
Externí odkaz:
http://arxiv.org/abs/2209.06630
Many nonlocal models have adopted Euclidean balls as the nonlocal interaction neighborhoods. When solving them numerically, it is sometimes convenient to adopt polygonal approximations of such balls. A crucial question is, to what extent such approxi
Externí odkaz:
http://arxiv.org/abs/2109.12485
The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error decompositi
Externí odkaz:
http://arxiv.org/abs/2107.10109
In this paper we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that w
Externí odkaz:
http://arxiv.org/abs/2104.05063
Publikováno v:
Journal of Algebra 595 (2022) 398-433
The algebraic study of special integral operators led to the notions of Rota-Baxter operators and shuffle products which have found broad applications. This paper carries out an algebraic study of general integral operators and equations, and shows t
Externí odkaz:
http://arxiv.org/abs/2008.06756