The Fourier transform in Schwartz space

Authors

  • Carlos Alberto Peña Miranda Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Calle Germán Amézaga N° 375 - Edificio Jorge Basadre, Lima, Perú. http://orcid.org/0000-0002-4339-4615
  • Elizabeth Cosi Cruz Estudios Generales, Universidad Norbert Wiener, Av. Petit Thouars 2021, Lince, Lima, Perú.

DOI:

https://doi.org/10.17268/sel.mat.2021.02.19

Keywords:

Fubini’s theorem, Banach space, Lebesgue integral.

Abstract

The objective of this work is to study some properties and applications of the Schwartz space. Initially, the Fourier transform is used to demonstrate the transform of the derivative and derivative of the transform.

Then the completeness of the Schwartz space is studied and some properties are demonstrated. Finally the Fourier inversion formula and Plancherel’s theorem are proved.

Author Biography

Carlos Alberto Peña Miranda, Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Calle Germán Amézaga N° 375 - Edificio Jorge Basadre, Lima, Perú.

Departamento Academicos de Matematica.

References

Adams RA. Sobolev Spaces. New York: Academic Press; 1975.

Brezis H. Functional Analysis, Sobolev Spaces and Partial Differential Equations. New York: Springer; 2011.

Cavalcanti MM. y Domingos Cavalcanti, V. N. Introducao á Teoria das distribucoes e aos Espacos de Sobolev. Maringá: Departamento de Matemática; 2009.

Kesavan S. Topics in Functional Analysis and Applications. New Delhi: Willey Easten Limited; 1990.

Medeiros LA, Milla MH. Espacos de Sobolev. Rio de Janeiro: UFRJ, IM; 2000.

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Published

2021-12-27

How to Cite

Peña Miranda, C. A., & Cosi Cruz, E. (2021). The Fourier transform in Schwartz space. Selecciones Matemáticas, 8(02), 423-436. https://doi.org/10.17268/sel.mat.2021.02.19

Issue

Vol. 8 No. 02 (2021): August - December

Section

Review

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