An index formula for groups of isometric linear canonical transformations

  • Anton Savin

    Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
  • Elmar Schrohe

    Leibniz University Hannover, Institute of Analysis, Welfengarten 1, 30167 Hannover, Germany
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Abstract

We define a representation of the unitary group U(n)U(n) by metaplectic operators acting on L2(Rn)L^2(\mathbb{R}^n) and consider the operator algebra generated by the operators of the representation and pseudodifferential operators of Shubin class. Under suitable conditions, we prove the Fredholm property for elements in this algebra and obtain an index formula.

Cite this article

Anton Savin, Elmar Schrohe, An index formula for groups of isometric linear canonical transformations. Doc. Math. 27 (2022), pp. 983–1013

DOI 10.4171/DM/890