Discrete Function Theory Based on Skew Weyl Relations
نویسندگان
چکیده
In this paper we construct the main ingredients of a discrete function theory in higher dimensions by means of a new “skew” type of Weyl relations. We will show that this new type overcomes the difficulties of working with standard Weyl relations in the discrete case. A Fischer decomposition, Euler operator, monogenic projection, and basic homogeneous powers will be constructed.
منابع مشابه
The Cauchy-Kovalevskaya Extension Theorem in Discrete Clifford Analysis
Discrete Clifford analysis is a higher dimensional discrete function theory based on skew Weyl relations. It is centered around the study of Clifford algebra valued null solutions, called discrete monogenic functions, of a discrete Dirac operator, i.e. a first order, Clifford vector valued difference operator. In this contribution, we establish a Cauchy-Kovalevskaya extension theorem for discre...
متن کاملDiscrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model
A discrete analog of a skew selfadjoint canonical (Zakharov-Shabat or AKNS) system with a pseudo-exponential potential is introduced. For the corresponding Weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices. As an application explicit solutions are obtained for the discrete integrable nonlinear equation corresponding to the isotropic Heisenbe...
متن کاملSkew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems
New formulas on the inverse problem for the continuous skewself-adjoint Dirac type system are obtained. For the discrete skewself-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. BorgMarchenko type uniqueness theorems are derived for both discrete and ...
متن کاملStress Analysis of Skew Nanocomposite Plates Based on 3D Elasticity Theory Using Differential Quadrature Method
In this paper, a three dimensional analysis of arbitrary straight-sided quadrilateral nanocomposite plates are investigated. The governing equations are based on three-dimensional elasticity theory which can be used for both thin and thick nanocomposite plates. Although the equations can support all the arbitrary straight-sided quadrilateral plates but as a special case, the numerical results f...
متن کاملElastic/plastic Buckling Analysis of Skew Thin Plates based on Incremental and Deformation Theories of Plasticity using Generalized Differential Quadrature Method
Abstract In this study, generalized differential quadrature analysis of elastic/plastic buckling of skew thin plates is presented. The governing equations are derived for the first time based on the incremental and deformation theories of plasticity and classical plate theory (CPT). The elastic/plastic behavior of plates is described by the Ramberg-Osgood model. The ranges of plate geometries...
متن کامل