Notes on Jan Maria Kisyński's life and scientific work

A. Bobrowski

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 3, pp. 123-133

Bibliographie

[1] Arendt W., Batty J. K., Hieber M., Neubrander F., Vector-Valued Laplace Transforms and Cauchy Problems, Birkhäuser, Basel, 2001 | DOI | MR | Zbl

[2] Arendt W., El-Mennaoui O., Kéyantuo V., “Local Integrated Semigroups: Evolution with Jumps of Regularity”, Journal of Mathematical Analysis and Applications, 186:2 (1994), 572–595 | DOI | MR | Zbl

[3] Berg C., Christensen J. P. R., Ressel P., Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions, Springer, N.Y., 1984 | DOI | MR | Zbl

[4] Bátkai A., Engel K.-J., “Abstract Wave Equations with Generalized Wentzell Boundary Conditions”, Journal of Differential Equations, 207:1 (2004), 1–20 | DOI | MR | Zbl

[5] Bobrowski A., “Integrated Semigroups and the Trotter–Kato Theorem”, Bulletin of the Polish Academy of Sciences Mathematics, 41 (1994), 297–304 | MR

[6] Bobrowski A., “On the Yosida Approximation and the Widder–Arendt Theorem”, Studia Mathematica, 124:3 (1997), 281–290 | DOI | MR | Zbl

[7] Bobrowski A., Convergence of One-Parameter Operator Semigroups In Models of Mathematical Biology and Elsewhere, Cambridge University Press, Cambridge, 2016 | DOI | MR | Zbl

[8] Chojnacki W., “On the Equivalence of a Theorem of Kisyński and the Hille–Yosida Generation Theorem”, Proceedings of the American Mathematical Society, 126:2 (1998), 491–497 | DOI | MR | Zbl

[9] Chojnacki W., “Multiplier Algebras, Banach Bundles, and One-Parameter Semigroups”, Annali della Scuola Normale Superiore di Pisa – Classe di Scienze, 28:2 (1999), 287–322 | MR | Zbl

[10] Chojnacki W., “On Operator-Valued Cosine Sequences on UMD Spaces”, Studia Mathematica, 199:3 (2010), 267–278 | DOI | MR | Zbl

[11] Chill R., Keyantuo V., Warma M., “Generation of Cosine Families on ${L}^p(0,1)$ by Elliptic Operators with Robin Boundary Conditions”, Functional Analysis and Evolution Equations, The Günter Lumer Volume, Birkhäuser, Basel, 2007, 113–130 | DOI | MR

[12] Cohen P. J., “Factorization in Group Algebras”, Duke Mathematical Journal, 26:2 (1959), 199–205 | DOI | MR | Zbl

[13] Davis M. H. A., Lectures on Stochastic Control and Nonlinear Filtering, Springer, N.Y., 1984 | MR | Zbl

[14] Davis M. H. A., Markov Processes and Optimization, Chapman and Hall, London, 1993 | MR

[15] Durrett R., Stochastic Calculus. A Practical Introduction, CRC Press, Boca Raton, 1996 | MR | Zbl

[16] Dynkin E. B., Markov Processes, v. I, II, Springer, Berlin–Göttingen–Heidelberg, 1965 | DOI | MR | Zbl

[17] Ethier S. N., Kurtz T. G., Markov Processes. Characterization and Convergence, Wiley, N.Y., 1986 | DOI | MR | Zbl

[18] Elstrodt J., Maß- und Integrationstheorie, Springer, Berlin–Heidelberg, 2005 (in German) | DOI | MR

[19] Engel K.-J., Nagel R., One-Parameter Semigroups for Linear Evolution Equations, Springer, N.Y., 2000 | MR | Zbl

[20] Ermakov S. M., Nekrutkin V. V., Sipin A. S., Random Processes for Classical Equations of Mathematical Physics, Kluwer Academic Publishers Group, Dordrecht, 1989 | DOI | MR | Zbl

[21] Fattorini H. O., “Ordinary Differential Equations in Linear Topological Spaces. I”, Journal of Differential Equations, 5 (1969), 72–105 | DOI | MR | Zbl

[22] Fattorini H. O., “Ordinary Differential Equations in Linear Topological Spaces. II”, Journal of Differential Equations, 6 (1969), 50–70 | DOI | MR | Zbl

[23] Fattorini H. O., Second Order Linear Differential Equations in Banach Spaces, North-Holland, Amsterdam, 1985 | MR | Zbl

[24] Freidlin M., Functional Integration and Partial Differential Equations, Princeton University Press, Princeton, 1985 | MR | Zbl

[25] Goldstein S., “On Diffusion by Discontinuous Movements, and on the Telegraph Equation”, The Quarterly Journal of Mechanics and Applied Mathematics, 1951, no. 4, 129–156 | DOI | MR | Zbl

[26] Goldstein J. A., Semigroups of Linear Operators and Applications, Oxford University Press, N.Y., 1985 | MR | Zbl

[27] Haase M., “The Group Reduction for Bounded Cosine Functions on UMD Spaces”, Mathematische Zeitschrift, 262:2 (2009), 281–299 | DOI | MR | Zbl

[28] Heyer H., Probability Measures on Locally Compact Groups, Springer, Berlin–Heidelberg, 1977 | DOI | MR | Zbl

[29] Hille E., Functional Analysis and Semi-Groups, American Mathematical Society, N.Y., 1948 | MR | Zbl

[30] Hennig B., Neubrander F., “On Representations, Inversions and Approximations of Laplace Transform in Banach Spaces”, Applicable Analysis, 49 (1993), 151–170 | DOI | MR | Zbl

[31] Hewitt E., Ross K. A., Abstract Harmonic Analysis, v. II, Structure and Analysis for Compact Groups. Analysis on Locally Compact Abelian Groups, Springer, Berlin–Heidelberg, 1970 | DOI | MR | Zbl

[32] Janssen A., Siebert E., “Convolution Semigroups and Generalized Telegraph Equations”, Mathematische Zeitschrift, 177:4 (1981), 519–532 | DOI | MR | Zbl

[33] Kac M., Some Stochastic Problems in Physics and Mechanics, Colloq. Lect., 2, Magnolia Petrolum, 1956

[34] Kisyński J., “Sur la méthode des approximations successives pour un systéme de $n$ équations à $n$ inconnues”, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys., 6 (1958), 683–687 (in French) | MR | Zbl

[35] Kisyński J., “Sur les equations differentielles dans les espaces de Banach”, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys., 7 (1959), 381–385 (in French) | MR | Zbl

[36] Kisyński J., “Convergence du type ${\cal L}$”, Colloquium Mathematicum, 7 (1959/1960), 205–211 (in French) | DOI | MR

[37] Kisyński J., “Sur les familles compactes de fonctions mesurables”, Colloquium Mathematicum, 7 (1959/1960), 221–235 (in French) | DOI | MR

[38] Kisyński J., “Sur les opérateurs de Green des problémes de Cauchy abstraits”, Studia Mathematica, 23 (1963/1964), 285–328 (in French) | DOI | MR

[39] Kisyński J., “On Temporally Inhomogeneous Equations of Evolution in Banach Spaces”, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys., 14 (1966), 623–626 | MR | Zbl

[40] Kisyński J., “A Proof of the Trotter–Kato Theorem on Approximation of Semigroups”, Colloquium Mathematicum, 18 (1967), 181–184 | DOI | MR | Zbl

[41] Kisyński J., “On the Generation of Tight Measures”, Studia Mathematica, 30 (1968), 141–151 | DOI | MR | Zbl

[42] Kisyński J., “On Second Order Cauchy's Problem in a Banach Space”, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys., 18:7 (1970), 371–374 | MR | Zbl

[43] Kisyński J., “On Operator-Valued Solutions of d'Alembert's Functional Equation. I”, Colloquium Mathematicum, 23 (1971), 107–114 | DOI | MR | Zbl

[44] Kisyński J., “On Cosine Operator Functions and One-Parameter Groups of Operators”, Studia Mathematica, 44 (1972), 93–105 | DOI | MR

[45] Kisyński J., “On Operator-Valued Solutions of d'Alembert's Functional Equation. II”, Studia Mathematica, 42 (1972), 43–66 | DOI | MR | Zbl

[46] Kisyński J., “On M. Kac's Probabilistic Formula for the Solutions of the Telegraphist's Equation”, Annales Polonici Mathematici, 29 (1974), 259–272 | DOI | MR | Zbl

[47] Kisyński J., “Semi-Groups of Operators and Some of Their Applications to Partial Differential Equations”, Control Theory and Topics in Functional Analysis, Internat. Sem., Internat. Centre Theoret. Phys. (Trieste, 1974), v. 3, International Atomic Energy Agency, Vienna, 1976, 305–405 | MR | Zbl

[48] Kisyński J., The Argument of a Lagrange Subspace and the Maslov Index, Preprint 202, Institute of Mathematics, Polish Academy of Sciences, 1979

[49] Kisyński J., “On Semigroups Generated by Differential Operators on Lie Groups”, Journal of Functional Analysis, 31:2 (1979), 234–244 | DOI | MR | Zbl

[50] Kisyński J., “On the Telegraph Equation with a Small Parameter”, Research Bulletin of Lublin University of Technology, 12 (1991), 14–27 (in Polish)

[51] Kisyński J., The Widder Spaces, Representations of the Convolution Algebra ${L}^1({\mathbb R}^+)$ and One Parameter Semigroups of Operators, Preprint 588, Institute of Mathematics, Polish Academy of Sciences, 1998, 36 pp. | MR

[52] Kisyński J., “On Cohen's Proof of the Factorization Theorem”, Annales Polonici Mathematici, 75:2 (2000), 177–192 | DOI | MR | Zbl

[53] Kisyński J., “On Fourier Transforms of Distribution Semigroups”, Journal of Functional Analysis, 242 (2007), 400–441 | DOI | MR | Zbl

[54] Kolmogorov A. N., “Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung”, Mathematische Annalen, 104:1 (1931), 415–458 (in German) | DOI | MR | Zbl

[55] Kolesnik A. D., “The Explicit Probability Distribution of the Sum of Two Telegraph Processes”, Stochastics and Dynamics, 15:2 (2015), 1550013, 32 pp. | DOI | MR | Zbl

[56] Krein S. G., Linear Differential Equations in Banach Space, American Mathematical Society, Providence, 1971 | MR

[57] Lions J.-L., Équations différentielles opérationnelles et problémes aux limites, Die Grundlehren der mathematischen Wissenschaften, Springer, Berlin–Góttingen–Heidelberg, 1961 (in French) | MR

[58] Lax P. D., Phillips R. S., Scattering Theory, Academic Press, N.Y., 1967 | MR | Zbl

[59] Natanson I. P., Theory of Functions of Real Variable, Gosudarstvennoe izdatel'stvo tekhnichesko-teoreticheskoy literatury, M., 1957 (in Russian) | MR

[60] Da Prato G., Giusti F., “Una carracterizzazione dei generatori di funzioni coseno astratte”, Bollettino dell'Unione Matematica Italiana, 22 (1967), 357–362 (in Italian) | MR | Zbl

[61] Pinsky M. A., Lectures on Random Evolutions, World Scientific, Singapore, 1991 | DOI | MR

[62] Rudnicki R., Tyran-Kamińska M., Piecewise Deterministic Processes in Biological Models, Springer International Publishing, 2017 | DOI | MR | Zbl

[63] Simon B., Quantum Mechanics for Hamiltonians Defined as Quadratic Forms, Princeton University Press, Princeton, 1971 | MR | Zbl

[64] Sova M., “Cosine Operator Functions”, Rozprawy Matematyczne, 49 (1966), 1–47 | MR

[65] Wentzell A. D., A Course in the Theory of Stochastic Processes, McGraw-Hill International Book, N.Y., 1981 | MR | Zbl

[66] Yosida K., Functional Analysis, Springer, Berlin, 1965 | MR | Zbl