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The Gabor wave front set in spaces of ultradifferentiable functions

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The Gabor wave front set in spaces of ultradifferentiable functions

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Boiti, C.; Jornet Casanova, D.; Oliaro, A. (2019). The Gabor wave front set in spaces of ultradifferentiable functions. Monatshefte für Mathematik. 188(2):199-246. https://doi.org/10.1007/s00605-018-1242-3

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Título: The Gabor wave front set in spaces of ultradifferentiable functions
Autor: Boiti, Chiara Jornet Casanova, David Oliaro, Alessandro
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
[EN] We consider the spaces of ultradifferentiable functions S as introduced by Bjorck (and its dual S) and we use time-frequency analysis to define a suitable wave front set in this setting and obtain several applications: ...[+]
Palabras clave: Gabor wave front set , Weighted Schwartz classes , Short-time Fourier transform , Gabor frames
Derechos de uso: Reserva de todos los derechos
Fuente:
Monatshefte für Mathematik. (issn: 0026-9255 )
DOI: 10.1007/s00605-018-1242-3
Editorial:
Springer-Verlag
Versión del editor: https://doi.org/10.1007/s00605-018-1242-3
Código del Proyecto:
info:eu-repo/grantAgreement/MINECO//MTM2016-76647-P/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIA/
info:eu-repo/grantAgreement/UNIFE//FAR2013/
info:eu-repo/grantAgreement/UNIFE//FAR2014/
Agradecimientos:
The authors were partially supported by the INdAM-Gnampa Project 2016 "Nuove prospettive nell'analisi microlocale e tempo-frequenza", by FAR2013, FAR2014 (University of Ferrara) and by the project "Ricerca Locale - Analisi ...[+]
Tipo: Artículo

References

Albanese, A., Jornet, D., Oliaro, A.: Quasianalytic wave front sets for solutions of linear partial differential operators. Integr. Equ. Oper. Theory 66, 153–181 (2010)

Albanese, A., Jornet, D., Oliaro, A.: Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non-quasianalytic classes. Math. Nachr. 285(4), 411–425 (2012)

Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6(21), 351–407 (1966) [+]
Albanese, A., Jornet, D., Oliaro, A.: Quasianalytic wave front sets for solutions of linear partial differential operators. Integr. Equ. Oper. Theory 66, 153–181 (2010)

Albanese, A., Jornet, D., Oliaro, A.: Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non-quasianalytic classes. Math. Nachr. 285(4), 411–425 (2012)

Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6(21), 351–407 (1966)

Boiti, C., Gallucci, E.: The overdetermined Cauchy problem for $$\omega $$ ω -ultradifferentiable functions. Manuscripta Math. 155(3-4), 419–448 (2018)

Boiti, C., Jornet, D.: A simple proof of Kotake–Narasimhan theorem in some classes of ultradifferentiable functions. J. Pseudo-Differ. Oper. Appl. 8(2), 297–317 (2017)

Boiti, C., Jornet, D.: A characterization of the wave front set defined by the iterates of an operator with constant coefficients. Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM 111(3), 891–919 (2017)

Boiti, C., Jornet, D., Juan-Huguet, J.: Wave front sets with respect to the iterates of an operator with constant coefficients. Abstr. Appl. Anal. 2014, 1–17 (2014). https://doi.org/10.1155/2014/438716

Boiti, C., Jornet, D., Oliaro, A.: Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms. J. Math. Anal. Appl. 446, 920–944 (2017)

Bonet, J., Meise, R., Melikhov, S.N.: A comparison of two different ways to define classes of ultradifferentiable functions. Bull. Belg. Math. Soc. Simon Stevin 14(3), 425–444 (2007)

Borwein, J.M., Lewis, A.S.: Convex Analysis and Nonlinear Optimization. Theory and Examples, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. Springer, New York (2006)

Braun, R.W., Meise, R., Taylor, B.A.: Ultradifferentiable functions and Fourier analysis. Result. Math. 17, 206–237 (1990)

Cappiello, M., Schulz, R.: Microlocal analysis of quasianalytic Gelfand–Shilov type ultradistributions. Complex Var. Elliptic Equ. 61(4), 538–561 (2016)

Carypis, E., Wahlberg, P.: Propagation of exponential phase space singularities for Schrödinger equations with quadratic Hamiltonians. J. Fourier Anal. Appl. 23(3), 530–571 (2017)

Christensen, O.: An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis. Springer, Berlin (2016)

Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators on non-quasianalytic classes of Beurling type. Studia Math. 167(2), 99–131 (2005)

Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators of Beurling type and the wave front set. J. Math. Anal. Appl. 340(2), 1153–1170 (2008)

Fieker, C.: $$P$$ P -Konvexität und $$\omega $$ ω -Hypoelliptizität für partielle Differentialoperatoren mit konstanten Koeffizienten. Diplomarbeit, Mathematischen Institut der Heinrich-Heine-Universität Düsseldorf (1993)

Gröchenig, K.: Foundations of Time-Frequency Analysis. Birkhäuser, Boston (2001)

Gröchenig, K., Zimmermann, G.: Spaces of test functions via the STFT. J. Funct. Spaces Appl. 2(1), 25–53 (2004)

Heil, C.: A Basis Theory Primer. Applied and Numerical Harmonic Analysis. Springer, New York (2011)

Hörmander, L.: Fourier integral operators. Acta Math. 127(1), 79–183 (1971)

Hörmander, L.: Quadratic hyperbolic operators. In: Cattabriga, L., Rodino, L. (eds.) Microlocal Analysis and Applications. Lecture Notes in Mathematics, pp. 118–160. Springer, Berlin (1991)

Hörmander, L.: The Analysis of Linear Partial Differential Operators, vol. I. Springer-Verlag, Berlin (1983)

Hörmander, L.: The Analysis of Linear Partial Differential Operators, vol. II. Springer-Verlag, Berlin (1983)

Hörmander, L.: The Analysis of Linear Partial Differential Operators, vol. III. Springer-Verlag, Berlin (1985)

Janssen, A.J.E.M.: Duality and biorthogonality for Weyl–Heisenberg frames. J. Fourier Anal. Appl. 1(4), 403–436 (1995)

Langenbruch, M.: Hermite functions and weighted spaces of generalized functions. Manuscripta Math. 119(3), 269–285 (2006)

Meise, R., Vogt, D.: Introduction to Functional Analysis. Oxford Science Publications, Clarendon Press, Oxford (1997)

Nakamura, S.: Propagation of the homogeneous wave front set for Schrödinger equations. Duke Math. J. 126, 349–367 (2005)

Nicola, F., Rodino, L.: Global Pseudo-Differential Calculus on Euclidean Spaces. Springer, Basel (2010)

Pilipović, S.: Tempered ultradistributions. Boll. U.M.I. B (7) 2(2), 235-251 (1988)

Prangoski, B.: Pseudodifferential operators of infinite order in spaces of tempered ultradistributions. J. Pseudo-Differ. Oper. Appl. 4(4), 495–549 (2013)

Pilipović, S., Prangoski, B.: Anti-Wick and Weyl quantization on ultradistribution spaces. J. Math. Pures Appl. 103(2), 472–503 (2015)

Rodino, L.: Linear Partial Differential Operators and Gevrey Spaces. World Scientific Publishing Co., Inc., River Edge, NJ (1993)

Rodino, L., Wahlberg, P.: The Gabor wave front set. Monatsh. Math. 173, 625–655 (2014)

Schulz, R., Wahlberg, P.: Microlocal properties of Shubin pseudodifferential and localization operators. J. Pseudo-Differ. Oper. Appl. 7(1), 91–111 (2016)

Schulz, R., Wahlberg, P.: Equality of the homogeneous and the Gabor wave front set. Commun. Partial Differ. Equ. 42(5), 703–730 (2017)

Shubin, M.A.: Pseudodifferential Operators and Spectral Theory. Springer-Verlag, Berlin (1987)

Sjöstrand, J.: Singularités analytiques microlocales. Astérisque 95, 1–166 (1982)

Toft, J.: The Bargmann transform on modulation and Gelfand–Shilov spaces, with applications to Toeplitz and pseudo-differential operators. J. Pseudo-Differ. Oper. Appl. 3(2), 145–227 (2012)

Toft, J.: Images of function and distribution spaces under the Bargmann transform. J. Pseudo-Differ. Oper. Appl. 8(1), 83–139 (2017)

Treves, F.: Topological vector spaces, distributions and kernels. Academic Press, New York (1967)

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