Duality theorems for polyanalytic functions
-
Fabrizio Colombo
,
Kamal Diki
Abstract
The goal of this paper is to give a characterization of the dual of the space of polyanalytic functions on the complement of a compact set K and vanishing at infinity. The class of polyanalytic functions generalizes holomorphic functions and serves as a middle ground between holomorphic functions in one complex variable and those in two complex variables. The duality result is also expressed in topological terms through a new class of infinite-order differential operators, which includes well-known families of operators like the Laplace and Helmholtz operators. Since the notion of polyanalytic function generalizes that of holomorphic function, the duality theorems established in this paper can be considered a non-trivial generalization of the Köthe–Grothendieck theorem.
Funding statement: The research of Kamal Diki is supported by the Research Foundation – Flanders (FWO) under grant number 1268123N.
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Rings of differential operators on (k,s)-th Tjurina algebras of singularities
- Cokernels of random matrix products and flag Cohen–Lenstra heuristic
- Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
- The L p -L q compactness of commutators of oscillatory singular integrals
- Determination of a pair of newforms from the product of their twisted central values
- Metrical properties of exponentially growing partial quotients
- Nonlinear operations and factorizations on a class of affine modulation spaces
- On algebraic degrees of certain exponential sums over finite fields
- The ranks of (a,b)-Fibonacci sequences and congruences for certain partition functions and Ramanujan's mock theta functions
- Dynamics of radial threshold solutions for generalized energy-critical Hartree equation
- Modular representations of GL2(𝔽𝑞) using calculus
- Bounding the number of p'-degree characters from below
- Existence and multiplicity of non-radial sign-changing solutions for a semilinear elliptic equation in hyperbolic space
- Duality theorems for polyanalytic functions
- Lower bounds for the number of number fields with Galois group GL2(𝔽ℓ)
- Cylindrical ample divisors on Du Val del Pezzo surfaces
Artikel in diesem Heft
- Frontmatter
- Rings of differential operators on (k,s)-th Tjurina algebras of singularities
- Cokernels of random matrix products and flag Cohen–Lenstra heuristic
- Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
- The L p -L q compactness of commutators of oscillatory singular integrals
- Determination of a pair of newforms from the product of their twisted central values
- Metrical properties of exponentially growing partial quotients
- Nonlinear operations and factorizations on a class of affine modulation spaces
- On algebraic degrees of certain exponential sums over finite fields
- The ranks of (a,b)-Fibonacci sequences and congruences for certain partition functions and Ramanujan's mock theta functions
- Dynamics of radial threshold solutions for generalized energy-critical Hartree equation
- Modular representations of GL2(𝔽𝑞) using calculus
- Bounding the number of p'-degree characters from below
- Existence and multiplicity of non-radial sign-changing solutions for a semilinear elliptic equation in hyperbolic space
- Duality theorems for polyanalytic functions
- Lower bounds for the number of number fields with Galois group GL2(𝔽ℓ)
- Cylindrical ample divisors on Du Val del Pezzo surfaces
