In preparation
- Fresnel integrable functions and Feynman path integrals
(with Sonia Mazzucchi and Fabio Nicola) - Phase space localization problems in quantum harmonic analysis
(with Franz Luef) - …
Preprints
P4. Mazzucchi, S.; Nicola, F.; Trapasso, S. Ivan.
Phase space analysis of finite and infinite dimensional Fresnel integrals.
arXiv:2403.20082
P3. Trapasso, S. Ivan.
Phase space analysis of spectral multipliers for the twisted Laplacian.
arXiv:2306.00592
P2. Alberti, Giovanni S.; Felisi, Alessandro; Santacesaria, Matteo; Trapasso, S. Ivan.
Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform.
arXiv:2302.03577
P1. Nicola, Fabio; Trapasso, S. Ivan.
On the stability of deep convolutional neural networks under irregular or random deformations.
arXiv:2104.11977
Journal articles
A14. Nicola, Fabio; Trapasso, S. Ivan.
Stability of the scattering transform for deformations with minimal regularity.
J. Math. Pures Appl. 180 (2023), pages 122-150.
DOI: 10.1016/j.matpur.2023.10.008 (open access) – arXiv:2205.11142
A13. Bhimani, Divyang G.; Manna, Ramesh; Nicola, Fabio; Thangavelu, Sundaram; Trapasso, S. Ivan.
On heat equations associated with fractional harmonic oscillators.
Fract. Calc. Appl. Anal. 26 (2023), 2470-2492.
DOI: 10.1007/s13540-023-00208-6 (open access) – arXiv:2210.07691
A12. Nicola, Fabio; Romero, José Luis; Trapasso, S. Ivan.
On the existence of optimizers for time-frequency concentration problems.
Calc. Var. 62, 21 (2023).
DOI: 10.1007/s00526-022-02358-6 (free access link) – arXiv:2112.09675
A11. Trapasso, S. Ivan.
On the convergence of a novel time-slicing approximation scheme for Feynman path integrals.
Int. Math. Res. Not. 2023, 18 (2023), pages 11930-11961.
DOI: 10.1093/imrn/rnac179 (free access link) – arXiv:2107.00886
A10. Bhimani, Divyang G.; Manna, Ramesh; Nicola, Fabio; Thangavelu, Sundaram; Trapasso, S. Ivan.
Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness.
Adv. Math. 392 (2021), 107995.
DOI: 10.1016/j.aim.2021.107995 – arXiv:2008.01226
A9. Cordero, Elena; Nicola, Fabio; Trapasso, S. Ivan.
Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators.
Appl. Comput. Harmon. Anal. 55 (2021), 405–425.
DOI: 10.1016/j.acha.2021.06.007 – arXiv:2005.03911
A8. Nicola, Fabio; Trapasso, S. Ivan.
A note on the HRT conjecture and a new uncertainty principle for the short-time Fourier transform.
J. Fourier Anal. Appl. 26 (2020), 68.
DOI: 10.1007/s00041-020-09769-z – arXiv:1911.12241
A7. Trapasso, S. Ivan.
Time-frequency analysis of the Dirac equation.
J. Differential Equations 269 (2020), no. 3, 2477–2502.
DOI: 10.1016/j.jde.2020.02.002 – arXiv:1909.09842
A6. Nicola, Fabio; Trapasso, S. Ivan.
On the pointwise convergence of the integral kernels in the Feynman-Trotter formula.
Comm. Math. Phys. 376 (2020), no. 3, 2277–2299.
DOI: 10.1007/s00220-019-03524-2 – arXiv:1904.12531
A5. Cordero, Elena; Trapasso, S. Ivan.
Linear perturbations of the Wigner distribution and the Cohen class.
Anal. Appl. 18 (2020), no. 3, 385–422.
DOI: 10.1142/S0219530519500052 – arXiv:1811.07795
A4. Nicola, Fabio; Trapasso, S. Ivan.
Approximation of Feynman path integrals with non-smooth potentials.
J. Math. Phys. 60 (2019), 102103.
DOI: 10.1063/1.5095852 – arXiv:1812.07487
A3. Cordero, Elena; D’Elia, Lorenza; Trapasso, S. Ivan.
Norm estimates for $\tau$-pseudodifferential operators in Wiener amalgam and modulation spaces.
J. Math. Anal. Appl. 471 (2019), no. 1-2, 541–563.
DOI: 10.1016/j.jmaa.2018.10.090 – arXiv:1803.07865
A2. Cordero, Elena; Nicola, Fabio; Trapasso, S. Ivan.
Almost diagonalization of $\tau$-pseudodifferential operators with symbols in Wiener amalgam and modulation spaces.
J. Fourier Anal. Appl. 25 (2019), no. 4, 1927–1957.
DOI: 10.1007/s00041-018-09651-z – arXiv:1802.10314
A1. D’Elia, Lorenza; Trapasso, S. Ivan.
Boundedness of pseudodifferential operators with symbols in Wiener amalgam spaces on modulation spaces.
J. Pseudo-Differ. Oper. Appl. 9 (2018), no. 4, 881–890.
DOI: 10.1007/s11868-017-0220-1 – arXiv:1703.08989
Books
B1. Nicola, Fabio; Trapasso, S. Ivan.
Wave Packet Analysis of Feynman Path Integrals.
Lecture Notes in Mathematics, vol. 2305, pp. XIII+214, Springer (2022).
DOI: 10.1007/978-3-031-06186-8
ISBN: 978-3-031-06185-1 (softcover) – 978-3-031-06186-8 (eBook)
Edita
E1. Cordero, Elena; Trapasso, S. Ivan (Eds.)
Microlocal and Time-Frequency Analysis.
Printed Edition of the Special Issue Published in Mathematics, pp. 140, MDPI (2022).
DOI: 10.3390/books978-3-0365-3172-4
ISBN: 978-3-0365-3173-1 (softcover) – 978-3-0365-3172-4 (eBook – open access PDF)
Book chapters, proceedings and expository papers
C5. Feichtinger, Hans G.; Nicola, Fabio; Trapasso, S. Ivan.
On exceptional times for pointwise convergence of integral kernels in Feynman-Trotter path integrals.
In: Anomalies in Partial Differential Equations, pp. 293-311, Springer-INDAM series (2021).
DOI: 10.1007/978-3-030-61346-4_13 – arXiv:2004.06017
C4. Trapasso, S. Ivan.
A time-frequency analysis perspective on Feynman path integrals.
In: Landscapes of Time-Frequency Analysis – ATFA 2019, pp. 175-202, Appl. Numer. Harmon. Anal., Birkhäuser (2020).
DOI: 10.1007/978-3-030-56005-8_10 – arXiv:2004.01784
C3. Rodino, Luigi; Trapasso, S. Ivan.
An introduction to the Gabor wave front set.
In: Anomalies in Partial Differential Equations, pp. 369-393, Springer-INDAM series (2021).
DOI: 10.1007/978-3-030-61346-4_17 – arXiv:2004.01290
C2. Bayer, Dominik; Cordero, Elena; Gröchenig, Karlheinz; Trapasso, S. Ivan.
Linear perturbations of the Wigner transform and the Weyl quantization.
In: Advances in Microlocal and Time-Frequency Analysis, pp. 79-120, Appl. Numer. Harmon. Anal., Birkhäuser (2020).
DOI: 10.1007/978-3-030-36138-9_5 – arXiv:1906.02503
C1. Trapasso, S. Ivan.
Almost Diagonalization of Pseudodifferential Operators.
In: Landscapes of Time-Frequency Analysis, pp. 323-342, Appl. Numer. Harmon. Anal., Birkhäuser (2019).
DOI: 10.1007/978-3-030-05210-2_14 – arXiv:2004.03253