Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Laplace and Dirac operators are rotation invariant operators which can be neatly expressed in (continuous) Euclidean Clifford analysis. ,  consider the discrete counterparts of these operators, i.e. the discrete Laplacian Δ or star-Laplacian and the discrete Dirac operator ?.  explicitly construct rotations operators for both of these differential operators (denoted by ?a, b and dR(ea, b) respectively) in the discrete Clifford analysis setting. The operators ?a, b satisfy the defining relations for so ( m , C ) and they are endomorphisms of the space H k of k-homogeneous (discrete) harmonic polynomials, hence expressing H k as a finite-dimensional so ( m , C ) -representation. Furthermore, the space M k of (discrete) k-homogeneous monogenic polynomials can likewise be expressed as so ( m , C ) -representation by means of the operators dR(ea, b).  will also consider rotations of discrete harmonic (resp. monogenic) distributions, in particular point-distributions, which will allow us to evaluate functions in a rotated point. To make the discrete rotations more visual,  explicitly calculate the rotation of general point-distributions in two dimensions, showing the behavior of such discrete rotations in relation to the continuous case.
['H. De Ridder', 'Tim Raeymaekers', 'Franciscus Sommen']
I am writing a research paper on a idea Rotations in discrete Clifford analysis
[{"from": "human", "value": "I am writing a research paper on a idea Rotations in discrete Clifford analysis"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Laplace and Dirac operators are rotation invariant operators which can be neatly expressed in (continuous) Euclidean Clifford analysis. ,  consider the discrete counterparts of these operators, i.e. the discrete Laplacian \u0394 or star-Laplacian and the discrete Dirac operator ?.  explicitly construct rotations operators for both of these differential operators (denoted by ?a, b and dR(ea, b) respectively) in the discrete Clifford analysis setting. The operators ?a, b satisfy the defining relations for so ( m , C ) and they are endomorphisms of the space H k of k-homogeneous (discrete) harmonic polynomials, hence expressing H k as a finite-dimensional so ( m , C ) -representation. Furthermore, the space M k of (discrete) k-homogeneous monogenic polynomials can likewise be expressed as so ( m , C ) -representation by means of the operators dR(ea, b).  will also consider rotations of discrete harmonic (resp. monogenic) distributions, in particular point-distributions, which will allow us to evaluate functions in a rotated point. To make the discrete rotations more visual,  explicitly calculate the rotation of general point-distributions in two dimensions, showing the behavior of such discrete rotations in relation to the continuous case."}]