Abstract
I use Ehrenpreis’ Fundamental Principle to reinterpret some results of Morimoto and Fujita (Hiroshima Math. J. 25:493–512, 1995) on analytic functionals on the complex light cone. I then show how these ideas can be used to generalize such results to the bicomplex and multicomplex setting.
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References
Baley Price, G.: An Introduction to Multicomplex Spaces and Functions. Dekker, New York (1991)
Berenstein, C.A., Struppa, D.C.: Complex analysis and convolution equations. In: Several Complex Variables V. Encyclopaedia of Mathematical Sciences, vol. 54, pp. 1–109. Springer, Berlin (1993)
Colombo, F., Sabadini, I., Struppa, D.C., Vajiac, A., Vajiac, M.: Singularities of functions of one and several bicomplex functions. Ark. Mat. 49, 277–294 (2011)
Colombo, F., Sabadini, I., Struppa, D.C., Vajiac, A., Vajiac, M.: Bicomplex hyperfunction theory. Ann. Mat. Pura Appl. 190, 247–261 (2011)
Ehrenpreis, L.: The fundamental principle for linear constant coefficients partial differential equations. In: Proc. Int. Symp. Linear Spaces, Jerusalem, pp. 161–174 (1960)
Ehrenpreis, L.: Fourier Analysis in Several Complex Variables. Wiley-Interscience, New York (1970)
Luna-Elizarraras, M.E., Shapiro, M., Struppa, D.C., Vajiac, A.: Bicomplex numbers and their elementary functions. CUBO 14, 61–80 (2012)
Morimoto, M., Fujita, K.: Analytic functionals and entire functionals on the complex light cone. Hiroshima Math. J. 25, 493–512 (1995)
Palamodov, V.P.: Linear Differential Operators with Constant Coefficients. Springer, Berlin (1970)
Struppa, D.C.: The fundamental principle for systems of convolution equations. Mem. Am. Math. Soc. 273, 1–167 (1983)
Struppa, D.C., Vajiac, A., Vajiac, M.: Remarks on holomorphicity in three settings: complex, quaternionic, and bicomplex. In: Hypercomplex Analysis and Applications. Trends in Mathematics, pp. 261–274. Birkhäuser, Basel (2010)
Struppa, D.C., Vajiac, A., Vajiac, M.: Holomorphy in multicomplex spaces. In: IWOTA 2010 Proceedings. Operator Theory: Advances and Applications, vol. 221, pp. 617–634. Birkhäuser, Basel (2012)
Struppa, D.C., Vajiac, A., Vajiac, M.: Ehrenpreis’ fundamental principle and analytic functionals on the complex light cone (in preparation)
Treves, F.: Topological Vector Spaces, Distributions and Kernels. Academic Press, New York (1975)
Vajiac, A., Vajiac, M.: Multicomplex hyperfunctions. Complex Var. Elliptic Equ. 57, 751–762 (2012)
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Struppa, D.C. (2013). A Note on Analytic Functionals on the Complex Light Cone. In: Gentili, G., Sabadini, I., Shapiro, M., Sommen, F., Struppa, D. (eds) Advances in Hypercomplex Analysis. Springer INdAM Series, vol 1. Springer, Milano. https://doi.org/10.1007/978-88-470-2445-8_7
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DOI: https://doi.org/10.1007/978-88-470-2445-8_7
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