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Noncommutative Cauchy integral formula [PDF]
Complex Analysis and Operator Theory, 2016 The aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for C^1 functions on a real alternative *-algebra.
Ghiloni, Riccardo +2 more
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Cauchy integral formulae in quaternionic hermitean clifford analysis [PDF]
Complex Analysis and Operator Theory, 2011 The theory of complex Hermitean Clifford analysis was developed recently as a refinement of Euclidean Clifford analysis; it focusses on the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean Dirac operators constituting a
Abreu Blaya, Ricardo +4 more
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SOLUTION TO A PARABOLIC DIFFERENTIAL EQUATION IN HILBERT SPACE VIA FEYNMAN FORMULA I
Моделирование и анализ информационных систем, 2015 A parabolic partial differential equation u′t (t, x) = Lu(t, x) is considered, where L is a linear second-order differential operator with time-independent coefficients, which may depend on x. We assume that the spatial coordinate x belongs to a finiteor
I. D. Remizov
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The Cauchy-Pompeiu integral formula in elliptic complex numbers [PDF]
Complex Variables and Elliptic Equations, 2011 The aim of this article is to give a generalization of the Cauchy-Pompeiu integral formula for functions valued in parameter-depending elliptic algebras with structure polynomial $X^2 + \beta X + \alpha$ where $\alpha$ and $\beta$ are real numbers.
Alayon-Solarz, D., Vanegas, C. J.
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Journal of Taibah University for Science, 2023 In this manuscript, we provide a generalization of the Cauchy integral to appropriate families of real-valued functions defined in [Formula: see text]. The results are motivated by a generalization of regulated functions. The foundational theory for this
Jorge E. Macias-Diaz +1 more
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Derivative and higher-order Cauchy integral formula of matrix functions
Open Mathematics, 2021 The derivative of a nn-order matrix function on the complex field is usually defined as a n2{n}^{2}-order matrix, which is not suitable for generalizing Cauchy integral formula of matrix functions to its higher-order derivative form. In this paper, a new
Huang Xiaojie, Liu Zhixiu, Wu Chun
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On Principal Fuzzy Metric Spaces
Mathematics, 2022 In this paper, we deal with the notion of fuzzy metric space (X,M,∗), or simply X, due to George and Veeramani. It is well known that such fuzzy metric spaces, in general, are not completable and also that there exist p-Cauchy sequences which are not ...
Valentín Gregori +3 more
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Integral equation characterization of the Feynman–Kac formula for a regime-switching diffusion
Results in Applied Mathematics, 2020 In this paper, we provide an integral equation characterization of the solution to a Cauchy problem associated to the Feynman–Kac formula for a regime-switching diffusion.
Adriana Ocejo
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On Problem of Internal Boundary Control for String Vibration Equation
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 The article deals with the vibration control problem described by one dimensional wave equation with integral type boundary condition. As usual, the initial and final moments of time for arbitrary displacements and velocities of the wave are specified ...
A.Kh. Attaev
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Holomorphy tests based on Cauchy’s integral formula [PDF]
Pacific Journal of Mathematics, 1995 In this paper, \(X\) is either \(\mathbb{C}\), the open unit disk \(\mathbb{D}\) or the open upper half-plane \(\mathbb{U}\). \(G\) denotes the group \(M(2)\) of rigid motions of \(\mathbb{C}\) in the first case and in the other cases the full group of conformal automorphisms of \(X\). Cauchy's integral formula gives for rectifiable loops \(\Gamma\) in
Cascante, Carmen, Pascuas, Daniel
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