124 citations · 452 across the 28 of their papers we have counts for
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Convergent Quantum Normal Forms, -symmetry and reality of the spectrum
Emanuela Caliceti, Sandro Graffi
A class of non-selfadjoint, $\PT$-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is expl…
Quadratic PT-symmetric operators with real spectrum and similarity to self-adjoint operators
Emanuela Caliceti, Sandro Graffi, Michael Hitrik +1
It is established that a PT-symmetric elliptic quadratic differential operator with real spectrum is similar to a self-adjoint operator precisely when the associated fundamental ma…
Geometric approach to the Hamilton-Jacobi equation and global parametrices for the Schrödinger propagator
Sandro Graffi, Lorenzo Zanelli
We construct a family of Fourier Integral Operators, defined for arbitrary large times, representing a global parametrix for the Schrödinger propagator when the potential is quadra…
A criterion for the reality of the spectrum of PT symmetric Schroedinger operators with complex-valued periodic potentials
E. Caliceti, S. Graffi
Consider in the \Sc operator family depending on the real parameter , where is a complex-valued but symmetric periodic potential. A…
Spectral analysis of transfer operators associated to Farey fractions
Claudio Bonanno, Sandro Graffi, Stefano Isola
The spectrum of a one-parameter family of signed transfer operators associated to the Farey map is studied in detail. We show that when acting on a suitable Hilbert space of analyt…
A uniform quantum version of the Cherry theorem
Carlos Villegas Blas, Sandro Graffi
Consider in the operator family . is the quantum harmonic oscillator with diophantine frequency vector $\om$, a bounded pseudodiffe…