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Self-duality, Pieri Formula and Cauchy Formulas
Self-duality (evaluation symmetry), which we are going to discuss below, is one of the most characteristic properties of Macdonald polynomials. In...
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A Local Cauchy Integral Formula for Slice-Regular Functions
We prove a local Cauchy-type integral formula for slice-regular functions. The formula is obtained as a corollary of a general integral...
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The tangential k-Cauchy–Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group
The tangential k -Cauchy–Fueter operator and k -CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the...
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Carleman’s Formula for Solutions of Generalized Cauchy–Riemann Systems in Multidimensional Spatial Domains
In this paper, we consider the restoration problem for solutions of the generalized Cauchy–Riemann system in a multidimensional spatial domain, using...
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Cauchy Formulae and Hardy Spaces in Discrete Octonionic Analysis
In this paper, we continue the development of a fundament of discrete octonionic analysis that is associated to the discrete first order...
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Confidence Disc and Square for the Cauchy Distributions
We construct a confidence region of parameters for a sample of size N from the Cauchy distributed random variables. Although the Cauchy distribution...
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The Cauchy Problem for the Degenerate Beam Vibration Equation
We study the Cauchy problem for a degenerate differential equation of beam vibrations. Using the generalized Erdélyi–Kober operator, possessing the...
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Cauchy type integrals and a boundary value problem in a complex Clifford analysis
Clifford analysis is an important branch of modern analysis; it has a very important theoretical significance and application value, and its...
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d’Alembert Formula for Poroelasticity System Described by Three Elastic Parameters
We consider the Cauchy problem for a one-dimensional homogeneous system of poroelasticity equations described by three elastic parameters in a...
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Formula di Itô
La formula di Itô è lo strumento più importante del calcolo differenziale stocastico. In questo capitolo ne presentiamo diverse versioni che...
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From Cauchy, via Martinelli–Bochner and Leray, to the Henkin–Ramirez kernel
We begin by recalling Enrique Ramirez’s days at the University of Göttingen in the late 1960s, and the roots of my connection to him and his work....
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Lax-Oleinik Formula
In this chapter we present the Lax-Oleinik Formula, that provides and an explicit formula for the solutions of the initial value problem when the...
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Cauchy Theory
In this chapter we will begin to see more manifestations of how the definition of the complex derivative imposes strong conditions on analytic...
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Hypercomplex Cauchy-Type Integral
In this chapter, we consider a certain hypercomplex Cauchy-type integral taking values in a three-dimensional harmonic algebra with two-dimensional...
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The Cauchy Problem for a Stochastic Parabolic Equation with an Argument Deviation
The Cauchy problem for a stochastic nonlinear equation of parabolic type with delay is considered. Using Green’s function, a formula is derived for...
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Perturbations of non-autonomous second-order abstract Cauchy problems
In this paper we present time-dependent perturbations of second-order non-autonomous abstract Cauchy problems associated to a family of operators...
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Cauchy Problem for the Nonlinear Liouville Equation in the Class of Periodic Infinite-Gap Functions
AbstractThe inverse spectral problem method is used to integrate the nonlinear Liouville equation in the class of periodic infinite-gap functions....
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Cauchy Problem for the Loaded Korteweg–de Vries Equation in the Class of Periodic Functions
AbstractThe inverse spectral problem method is applied to finding a solution of the Cauchy problem for the loaded Korteweg–de Vries equation in the...
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Cauchy Theorem for a Surface Integral in a Finite-Dimensional Commutative Algebra
It is well known that in the case where a simply connected domain has a closed piecewise smooth boundary, spatial analogs of the Cauchy integral...