Octonionic monogenic and slice monogenic Hardy and Bergman spaces
-
Fabrizio Colombo
and
Irene Sabadini
Abstract
In this paper we discuss some basic properties of octonionic Bergman and Hardy spaces. In the first part we review some fundamental concepts of the general theory of octonionic Hardy and Bergman spaces together with related reproducing kernel functions in the monogenic setting. We explain how some of the fundamental problems in well-defining a reproducing kernel can be overcome in the non-associative setting by looking at the real part of an appropriately defined para-linear octonion-valued inner product. The presence of a weight factor of norm 1 in the definition of the inner product is an intrinsic new ingredient in the octonionic setting. Then we look at the slice monogenic octonionic setting using the classical complex book structure. We present explicit formulas for the slice monogenic reproducing kernels for the unit ball, the right octonionic half-space and strip domains bounded in the real direction. In the setting of the unit ball we present an explicit sequential characterization which can be obtained by applying the special Taylor series representation of the slice monogenic setting together with particular octonionic calculation rules that reflect the property of octonionic para-linearity.
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Articles in the same Issue
- Frontmatter
- The C*-algebra of the Boidol group
- Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order
- Positive rigs
- Torus bundles over lens spaces
- Topological amenability of semihypergroups
- On projections of the tails of a power
- Li–Yorke chaos for composition operators on Orlicz spaces
- A note on the post quantum-Sheffer polynomial sequences
- Finite rigid sets of the non-separating curve complex
- Building planar polygon spaces from the projective braid arrangement
- Octonionic monogenic and slice monogenic Hardy and Bergman spaces
- Transcendence on algebraic groups
- An explicit version of Bombieri’s log-free density estimate and Sárközy’s theorem for shifted primes
- The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras
- Joint distribution of the cokernels of random p-adic matrices II
Articles in the same Issue
- Frontmatter
- The C*-algebra of the Boidol group
- Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order
- Positive rigs
- Torus bundles over lens spaces
- Topological amenability of semihypergroups
- On projections of the tails of a power
- Li–Yorke chaos for composition operators on Orlicz spaces
- A note on the post quantum-Sheffer polynomial sequences
- Finite rigid sets of the non-separating curve complex
- Building planar polygon spaces from the projective braid arrangement
- Octonionic monogenic and slice monogenic Hardy and Bergman spaces
- Transcendence on algebraic groups
- An explicit version of Bombieri’s log-free density estimate and Sárközy’s theorem for shifted primes
- The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras
- Joint distribution of the cokernels of random p-adic matrices II
