Published

2024-07-18

The Principal Symbol Map for Lagrangian Distributions with Complex Phase

Símbolo principal para distribuciones Lagrangianas con función de fase compleja

DOI:

https://doi.org/10.15446/recolma.v57n2.115846

Keywords:

Lagrangian distribution, complex phase function, principal symbol (en)
distribuciones Lagrangianas, función de fase compleja, símbolo principal. (es)

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Authors

  • Gisel Mattar Marriaga University of Goettingen

The present paper focus on Lagrangian distributions with complex phase. We provide an alternative construction of their principal symbol map, which allows us to compute the principal symbol after clean composition of Fourier integral operators with complex phase.

El presente artículo se centra en el estudio de las distribuciones lagrangianas con fase compleja. Proponemos una construcción alternativa del símbolo principal, que nos permite calcular el símbolo principal de la distribución resultante de la composición de operadores integrales de Fourier con fase compleja.

References

J. J. Duistermaat, Fourier integral operators.

L. Hörmander, Fourier integral operators. I, Acta Mathematica 127 (1971), 79-183.

L. Hörmander, l2 estimates for fourier integral operators with complex phase, Arkiv för matematik 21 (1983), no. 1, 283-307.

L. Hörmander, The analysis of linear partial differential operators iv: Fourier integral operators, vol. 17, Springer, 2009.

A. Melin and J. Sjöstrand, Fourier integral operators with complex-valued phase functions, Fourier integral operators and partial differential equations, Springer, 1975, pp. 120-223.

A. Melin and J. Sjöstrand, Fourier integral operators with complex phase functions and parametrix for an interior boundary value problem, Communications in Partial Differential Equations 1 (1976), no. 4, 313-400.

E. T. Michael, Rayleigh waves in linear elasticity as a propagation of singularities phenomenon, Proc. Conf. on PDE and Geometry, Marcel Dekker, New York, 1979, pp. 273-291.

F. Trèves, Introduction to pseudodifferential and fourier integral operators. volume 2: Fourier integral operators, vol. 2, Springer Science & Business Media, 1980.

M. Zworski, Semiclassical analysis, vol. 138, American Mathematical Soc., 2012.

How to Cite

APA

Mattar Marriaga, G. (2024). The Principal Symbol Map for Lagrangian Distributions with Complex Phase. Revista Colombiana de Matemáticas, 57(2), 155–177. https://doi.org/10.15446/recolma.v57n2.115846

ACM

[1]
Mattar Marriaga, G. 2024. The Principal Symbol Map for Lagrangian Distributions with Complex Phase. Revista Colombiana de Matemáticas. 57, 2 (Jul. 2024), 155–177. DOI:https://doi.org/10.15446/recolma.v57n2.115846.

ACS

(1)
Mattar Marriaga, G. The Principal Symbol Map for Lagrangian Distributions with Complex Phase. rev.colomb.mat 2024, 57, 155-177.

ABNT

MATTAR MARRIAGA, G. The Principal Symbol Map for Lagrangian Distributions with Complex Phase. Revista Colombiana de Matemáticas, [S. l.], v. 57, n. 2, p. 155–177, 2024. DOI: 10.15446/recolma.v57n2.115846. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/115846. Acesso em: 22 jan. 2025.

Chicago

Mattar Marriaga, Gisel. 2024. “The Principal Symbol Map for Lagrangian Distributions with Complex Phase”. Revista Colombiana De Matemáticas 57 (2):155-77. https://doi.org/10.15446/recolma.v57n2.115846.

Harvard

Mattar Marriaga, G. (2024) “The Principal Symbol Map for Lagrangian Distributions with Complex Phase”, Revista Colombiana de Matemáticas, 57(2), pp. 155–177. doi: 10.15446/recolma.v57n2.115846.

IEEE

[1]
G. Mattar Marriaga, “The Principal Symbol Map for Lagrangian Distributions with Complex Phase”, rev.colomb.mat, vol. 57, no. 2, pp. 155–177, Jul. 2024.

MLA

Mattar Marriaga, G. “The Principal Symbol Map for Lagrangian Distributions with Complex Phase”. Revista Colombiana de Matemáticas, vol. 57, no. 2, July 2024, pp. 155-77, doi:10.15446/recolma.v57n2.115846.

Turabian

Mattar Marriaga, Gisel. “The Principal Symbol Map for Lagrangian Distributions with Complex Phase”. Revista Colombiana de Matemáticas 57, no. 2 (July 18, 2024): 155–177. Accessed January 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/115846.

Vancouver

1.
Mattar Marriaga G. The Principal Symbol Map for Lagrangian Distributions with Complex Phase. rev.colomb.mat [Internet]. 2024 Jul. 18 [cited 2025 Jan. 22];57(2):155-77. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/115846

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