Abstract
We study the biorthogonal Appell system and Kondrat’ev spaces in the case where the parameter of a μ-exponential is perturbed by holomorphic invertible functions. The results obtained are applied to the investigation of pseudodifferential equations.
Similar content being viewed by others
References
Yu. L. Daletskii, “A biorthogonal analog of Hermitian polynomials and the conversion of Fourier transformation in non-Gaussian measure,” Funk. Anal. Prilozh., 25, No. 2, 68–70 (1991).
S. Albeverio, Yu. Kondratiev, and L. Streit, “How to generalize white noise analysis to non-Gaussian spaces,” in: Ph. Beancard et al. (editors), Dynamics of Complex and Irregular Systems, World Scientific (1993).
S. Albeverio, Yu. Daletzky, Yu. Kondratiev, and L. Streit, Non-Gaussian Infinite-Dimensional Analysis, SFB, 237, Preprint No. 217, Inst. Math. Ruhr-Universität-Bochum (1994).
Yu. Kondratiev, L. Streit, W. Westerkamp, and J. Yan, Generalized Functions in Infinite Dimensional Analysis, Preprint BiBoS 369/6/95 (1995).
Yu. Kondratiev and L. Streit, “Spaces of white noise distributions: constructions, descriptions, applications. I,” Rept. Math. Phys., 33, 341–366 (1993).
Yu. M. Berezanskii and Yu. G. Kondrat’ev, Spectral Methods in Infinite-Dimensional Analysis [in Russian], Naukova Dumka, Kiev (1988).
S. Dineen, Complex Analysis in Locally Convex Spaces, Math. Studies, 57, North Holland, Amsterdam (1981).
E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Am. Math. Soc., Providence (1957).
N. Dunford and J. T. Schwartz, Linear Operators. Part 1: General Theory, Vol. 1, Interscience, New York (1958).
Yu. Kondrat’ev, L. Streit, and G. Us, Generalized Appell Systems in Infinite-Dimensional Analysis, Preprint, BiBoS 820/12/95 (1995).
G. F. Us, “Dual Appell systems in Poissonian analysis,” Meth. Funct. Anal. Topol., 1, 93–108 (1995).
Yu. Kondratiev, P. Leukert, and L. Streit, Wick Calculus in Gaussian Analysis, Preprint, BiBoS 637.94 (1994).
Additional information
Ukrainian National Technical University “Kiev Polytechnical Institute.” Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 4, pp. 527–534, April, 1997.
Rights and permissions
About this article
Cite this article
Kachanovskii, N.A. Dual Appell system and Kondrat’ev spaces in analysis on Schwartz spaces. Ukr Math J 49, 581–589 (1997). https://doi.org/10.1007/BF02487321
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487321