This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bers, L.: Theory of Pseudo-Analytic Functions, Courant Institute, New York, 1953.
Begehr, H., and Gilbert, R.P.: Randwertaufgaben ganzzahliger Charakteristik für verallgemeinerte hyperanalytische Funktionen, Applicable Analysis, Vol. 6, 189–205, 1977.
Begehr, H., and Gilbert, R. P.: On Riemann boundary value problems for certain linear elliptic systems in the plane, J. Diff. Equats. 32, (1979) 1–14.
Begehr, H., and Gilbert R.P.: Piecewise continuous solutions of pseudoparabolic equations in two space dimensions, Proc. Royal Soc. Edinburgh, 81A, (1978) 153–173.
Bojarski, B.B.: The theory of generalized analytic vectors (in Russian), Annales Polonici Mathematici, 17 (1966), 281–320.
Buchanan, J. and Gilbert, R.P.: The Hilbert problem for hyperanalytic functions, Applied Math. Inst. Tech. Report No. 66A.
Douglis, A.: A function-theoretic approach to elliptic systems of equations in two variables, Comm. Pure. Applied Math., 6 (1953) 259–289.
Gilbert, R.P.: Constructive Methods for Elliptic Equations, Lecture Notes in Math. No. 365, Springer, Berlin, 1974.
Gilbert, R.P. and Hile, G.: Generalized hypercomplex function theory, Trans. Am. Math. Soc., 195 (1974), 1–29.
Gilbert, R.P. and Hile, G.: Hypercomplex function theory in the sense of L. Bers, Math. Machrichten, 72 (1976), 187–200.
Gilbert, R.P. and Hile, G.: Hilbert function modules with reproducing kernels, Nonlinear Analysis, 1 (1977), 135–150.
Gilbert, R.P. and Schneider, M.: Generalized meta and pseudoparabolic equations in the plane, Memorial Volume in Honor of I.N. Vekua, Moscow, 1978.
Gilbert, R.P. and Wendland, W.: Analytic, generalized hyperanalytic function theory and an application to elasticity, Proc. Royal Soc. Edinburgh, 73A (1975), 317–331.
Haack, W., and Wendland, W.: Lectures on Partial and Pfaffian Differential Equations, Pergamon London, 1972.
Habetha, K.: On zeros of elliptic systems of first order in the plane, in "Function Theoretic Methods in Differential Equations," Pitman, London, 1976.
Hile, G.: Hypercomplex function theory applied to partial differential equations. Ph.D. Dissertation, Indiana University (1972).
Hile, G., and Protter, M.: Maximum principles for a class of first-order elliptical systems, J. Diff. Equats., 24 (1977), 136–151.
Kühn, E.: Über die Funktionentheoric und das Ähnlichkeitsprinzip einer Klasse elliptischer Differentialgleichungssysteme in der Ebene, Dissertation, Dortmund, 1974.
Miranda, C.: Partial Differential Equations of Elliptic Type, Springer, Berlin, 1970.
Orton, M.: Hilbert transforms, Plemelj relations, and Fourier transforms of distributions, SIAM J. Math. Anal. 4 (1973), 656–670.
Orton, M.: Hilbert boundary value problems — a distributional approach, Proc. Royal Soc. Edinburgh, 76, (1977) 193–208.
Pascali, D.: Vecteurs analytiques généralisés, Rev. Roum. Math. pura appl., 10 (1965), 779–808.
Tutschke, W.: Partielle Komplexe Differentialgleichungen VEB, Berlin, 1977.
Vekua, I.N.: Generalized Analytic Functions, Pergamon, London, 1962.
Wendland, W.: Elliptic Systems in the Plane, Pitman, London, 1979.
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Gilbert, R.P. (1981). Generalized hyperanalytic function theory. In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089832
Download citation
DOI: https://doi.org/10.1007/BFb0089832
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10569-5
Online ISBN: 978-3-540-38538-7
eBook Packages: Springer Book Archive