What question did this study set out to answer?

The research aims to establish the boundedness of biinvariant functions on the Olshanski spherical pair.

March 29, 2026Open Access

On Functions of Negative Type on the Olshanski Spherical Pair (SL(∞), SU(∞))

Key Points

The research aims to establish the boundedness of biinvariant functions on the Olshanski spherical pair.
Utilized a generalized Bochner type representation for Olshanski spherical pairs
Analyzed continuous functions on SL(∞)
Focused on functions with negative type
Investigated the implications of biinvariance under SU(∞)
Demonstrated that every SU-bi-invariant continuous function of negative type is bounded
Provided evidence for the relationship between negative type and boundedness
Established key results in the context of infinite dimensional analysis

Abstract

In this paper, using a generalized Bochner type representation for Olshanski spherical pairs, we prove the boundedness of every SU () -biinvariant continuous function of negative type on the infinite dimensional special linear group SL() .

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