Fourier Theory Under Möbius Transformations

Ji, Xinhua; Qian, Tao; Ryan, John

doi:10.1007/978-1-4612-1374-1_4

Cited by 7 publications

(3 citation statements)

References 20 publications

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“…In analogy to the papers [10,14,15] and others, the property B Ξ,ρT = CT M •W T •B Ω •W T −1 • C T −1 M means that the θ-hyperholomorphic Bergman projection may be called conformally covariant. Similarly, the equality B Ξ,ρT (z, ξ) = C T (z)B Ω (T (z), T (ξ))C T (ξ) means that the θ-hyperholomorphic Bergman kernel can be called conformally invariant.…”

Section: Corollary 410 the θ-Hyperholomorphic Bergman Projection Asmentioning

confidence: 91%

“…Similarly, the equality B Ξ,ρT (z, ξ) = C T (z)B Ω (T (z), T (ξ))C T (ξ) means that the θ-hyperholomorphic Bergman kernel can be called conformally invariant. Note also that Corollary 4.4 is an analogue for the Bergman spaces of the respective fact for Hardy spaces, obtained as Proposition 4 in [10].…”

Section: Corollary 410 the θ-Hyperholomorphic Bergman Projection Asmentioning

confidence: 92%

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Hyperholomorphic Bergman Spaces and Bergman Operators Associated with Domains in $${\mathbb{C}}^2$$

González-Cervantes¹,

Shapiro²

2008

Complex anal.oper. theory

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The work deals with a version of quaternionic analysis adapted in such a way that the set of arising hyperholomorphic functions includes, as a proper subset, all holomorphic mappings. There are considered, for the theory of the corresponding Bergman spaces and Bergman operators, both classic, commonly treated aspects and more specific ones, in particular, conformally invariant or covariant character of certain objects; a description of an algebra generated by the Bergman projection together with a criterion ensuring the Fredholmness of elements of the algebra; relations with the usual holomorphic mappings theory in two complex variables are demonstrated as well. Mathematics Subject Classification (2000). 30G35, 32A25, 47B32, 47B37, 47L30.

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Section: Corollary 410 the θ-Hyperholomorphic Bergman Projection Asmentioning

confidence: 91%

Section: Corollary 410 the θ-Hyperholomorphic Bergman Projection Asmentioning

confidence: 92%

Hyperholomorphic Bergman Spaces and Bergman Operators Associated with Domains in $${\mathbb{C}}^2$$

González-Cervantes¹,

Shapiro²

2008

Complex anal.oper. theory

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“…In analogy to the papers [3], [4], [5], and others, the property (2.1.1) means that the ψ-hyperholomorphic Bergman kernel may be called conformally invariant. Similarly, the property (2.1.2) means that the ψ-hyperholomorphic Bergman projection may be called conformally covariant.…”

mentioning

confidence: 99%

On Some Categories and Functors in the Theory of Quaternionic Bergman Spaces

González-Cervantes¹,

Luna-Elizarrarás²,

Shapiro³

2009

AACA

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Basic facts are presented about the theory of quaternionic Bergman spaces with special emphasis on what is happening with them under conformal transformations of the domains. Constructing a series of categories of quaternion-valued functions as well as functors acting between them we show that the arising spaces and operators have conformally covariant or invariant characters in terms of the theory of categories.

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On the Geometry of the Quaternionic Unit Disc

Bisi

Gentili

2010

Hypercomplex Analysis and Applications

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). The session proved to be particularly lively, as it hosted more than 35 speakers, and showed how the topic of hypercomplex analysis is fertile. The contents of the contributions cover several different aspects of hypercomplex analysis, ranging from Clifford analysis on superspace to the study of Dirac operators on surfaces, Dunkl monogenic functions, and applications, for example, to operator theory. The contributions represent the most recent achievements in the area and have been refereed.

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Fourier Theory Under Möbius Transformations

Cited by 7 publications

References 20 publications

Hyperholomorphic Bergman Spaces and Bergman Operators Associated with Domains in $${\mathbb{C}}^2$$

Hyperholomorphic Bergman Spaces and Bergman Operators Associated with Domains in $${\mathbb{C}}^2$$

On Some Categories and Functors in the Theory of Quaternionic Bergman Spaces

On the Geometry of the Quaternionic Unit Disc

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