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Bürger, R.: On the maintenance of genetic variation: Global analysis of Kimura's continuum-of-alleles model. J. Math. Biol.24, 341–351 (1986)
Bürger, R.: The maintenance of genetic variation: A functional analytic approach to quantitative genetic models. In: de Jong, G. (ed.) Population Genetics and Evolution. Berlin Heidelberg New York: Springer 1987 (In press)
Crow, J.F., Kimura, M.: An introduction to population genetics theory. New York: Harper and Row 1970
Feichtinger, H.G.: Compactness in translation invariant Banach spaces of distributions and compact multipliers. J. Math. Anal. Appl.102, 289–327 (1984)
Fleming, W.H.: Equilibrium distributions of continuous polygenic traits. SIAM J. Appl. Math.36, 148–168 (1979)
Greiner, G.: A typical Perron-Frobenius theorem with applications to an age-dependent population equation. In: Kappel, F., Schappacher, W. (eds.) Infinite-dimensional systems. Lect. Notes Math. 1076. Berlin Heidelberg New York: Springer 1984
Henry, D.: Geometric theory of semilinear parabolic equations. Lect. Notes Math. 840. Berlin Heidelberg New York: Springer 1981
Jörgens, K.: Lineare Integraloperatoren. Stuttgart: BG Teubner 1970
Kato, T.: Perturbation theory of linear operators. Berlin Heidelberg New York: Springer 1966
Kimura, M.: A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proc. Natl. Acad. Sci. USA54, 731–736 (1965)
Kingman, J.F.C.: On the properties of bilinear models for the balance between mutation and selection. Math. Proc. Camb. Phil. Soc.81, 443–453 (1977)
Kingman, J.F.C.: A simple model for the balance between selection and mutation. J. Appl. Probab.15, 1–12 (1978)
Moran, P.A.P.: Global stability of genetic systems governed by mutation and selection. Math. Proc. Camb. Phil. Soc.80, 331–336 (1976)
Moran, P.A.P.: Global stability of generic systems governed by mutation and selection II. Math. Proc. Camb. Phil. Soc.81, 435–441 (1977)
Nagel, R. (ed.): One-parameter semigroups of positive operators. Lect. Notes Math. 1184. Berlin Heidelberg New York: Springer 1986
Nagylaki, T.: Selection on a quantitative character. In: Chakravarti, A. (ed.) Human population genetics: The Pittsburgh Symposium. New York: Van Nostrand 1984
Newburgh, J.D.: The variation of spectra. Duke Math. J.18, 165–176 (1951)
Pazy, A.: Semigroups of linear operators and applications to partial differential equations. New York Heidelberg Berlin: Springer 1983
Schaefer, H.H.: Banach lattices and positive operators. Berlin Heidelberg New York: Springer 1974
Steinberg, S.: Meromorphic families of compact operators. Arch. Rational Mech. Anal.31, 372–379 (1968)
Turelli, M.: Heritable genetic variation via mutation-selection balance: Lech's Zeta meets the abdominal bristle. Theor. Popul. Biol.25, 138–193 (1984)
Voigt, J.: A perturbation theorem for the essential spectral radius of strongly continuous semigroups. Monatsh. Math.90, 153–161 (1980)
Yosida, K.: Functional analysis. 5th ed. Berlin Heidelberg New York: Springer 1978
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Bürger, R. Perturbations of positive semigroups and applications to population genetics. Math Z 197, 259–272 (1988). https://doi.org/10.1007/BF01215194
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DOI: https://doi.org/10.1007/BF01215194