Abstract
We obtain formulas for the asymptotic expansion of the Berezin transform on symmetric spaces in terms of invariant differential operators associated with the Peter-Weyl decomposition under the maximal compact subgroup. A unified treatment makes it possible to derive the formulas for the complex (hermitian) as well as for the real case, and for all types of symmetric spaces (non-compact, compact and flat).
Mathematics Subject Classification (2000). Primary 32M15; Secondary 46E22, 53C35.
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Engliš, M., Upmeier, H. (2012). Real Berezin Transform and Asymptotic Expansion for Symmetric Spaces of Compact and Non-compact Type. In: Ball, J., Curto, R., Grudsky, S., Helton, J., Quiroga-Barranco, R., Vasilevski, N. (eds) Recent Progress in Operator Theory and Its Applications. Operator Theory: Advances and Applications(), vol 220. Springer, Basel. https://doi.org/10.1007/978-3-0348-0346-5_6
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DOI: https://doi.org/10.1007/978-3-0348-0346-5_6
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