Quantum theta functions and signal analysis

Representations of the celebrated Heisenberg commutation relations and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis).  In this talk I explain how Heisenberg relations bridge the noncommutative geometry and signal analysis.  After providing a brief comparative dictionary of the two languages, I will show e.g. that the Janssen representation of Gabor frames with generalized Gaussians as Gabor atoms yields in a natural way quantum theta functions, and that the Rieffel scalar product and associativity relations underlie both the functional equations for quantum thetas and the fundamental Identity of Gabor analysis.

The talk is based on joint work with F. Luef.