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The Monomiality Approach to Multi-Index Polynomials in Several Variables
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Carlo Belingeri
Published/Copyright:
March 10, 2010
Abstract
The monomiality principle was introduced (see [Dattoli, Hermite–Bessel and Laguerre–Bessel functions: a by-product of the monomiality principle: 147–164, Aracne, 2000] and the references therein) in order to derive the properties of special or generalized polynomials starting from the corresponding ones of monomials. We show a general technique of extending the monomiality approach to multi-index polynomials in several variables. Application of this technique to the case of Hermite, Laguerre-type and mixed-type (i.e., between Laguerre and Hermite) polynomials is given.
Key words and phrases:: Exponential operators; operational calculus; monomiality principle; Gould–Hopper polynomials; multi-index Hermite and Laguerre polynomials
Received: 2006-07-13
Published Online: 2010-03-10
Published in Print: 2007-March
© Heldermann Verlag
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Articles in the same Issue
- The Cauchy Transform for the Hodge/De Rham System and Some of its Properties
- Explicit Bounds for Composition Operators Preserving BMO(ℝ)
- A Dirichlet Problem for the Inhomogeneous Polyharmonic Equation in the Upper Half Plane
- The Monomiality Approach to Multi-Index Polynomials in Several Variables
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- Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients
- Generating Relations of Hermite–Tricomi Functions Using a Representation of Lie Algebra 𝑇3
- Near Field Representations of the Acoustic Green's Function in a Shallow Ocean with Fluid-Like Seabed
- An Initial-Boundary Value Problem for a Viscous Compressible Flow
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Keywords for this article
Exponential operators;
operational calculus;
monomiality principle;
Gould–Hopper polynomials;
multi-index Hermite and Laguerre polynomials
Articles in the same Issue
- The Cauchy Transform for the Hodge/De Rham System and Some of its Properties
- Explicit Bounds for Composition Operators Preserving BMO(ℝ)
- A Dirichlet Problem for the Inhomogeneous Polyharmonic Equation in the Upper Half Plane
- The Monomiality Approach to Multi-Index Polynomials in Several Variables
- On the Global and Local Solution of the Multidimensional Darboux Problem for Some Nonlinear Wave Equations
- Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients
- Generating Relations of Hermite–Tricomi Functions Using a Representation of Lie Algebra 𝑇3
- Near Field Representations of the Acoustic Green's Function in a Shallow Ocean with Fluid-Like Seabed
- An Initial-Boundary Value Problem for a Viscous Compressible Flow
- On the Measurability of Additive Functionals
- On BVPS for Strongly Elliptic Systems with Higher Order Boundary Conditions
- An Example of Fractal Singular Homogenization
- Solution of a Goursat Problem in Optimal Domains
