Volume 11, no. 3Pages 123 - 133

Notes on Jan Maria Kisynski's Life and Scientific Work

A. Bobrowski
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References
1. Arendt W., Batty J.K., Hieber M., Neubrander F. Vector-Valued Laplace Transforms and Cauchy Problems. Basel, Birkhauser, 2001. DOI: 10.1007/978-3-0348-5075-9
2. Arendt W., El-Mennaoui O., Keyantuo V. Local Integrated Semigroups: Evolution with Jumps of Regularity. Journal of Mathematical Analysis and Applications, 1994, vol. 186, no. 2, pp. 572-595. DOI: 10.1006/jmaa.1994.1318
3. Berg C., Christensen J.P.R., Ressel P. Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions. N.Y., Springer, 1984. DOI: 10.1007/978-1-4612-1128-0
4. Batkai A., Engel K.-J. Abstract Wave Equations with Generalized Wentzell Boundary Conditions. Journal of Differential Equations, 2004, vol. 207, no. 1, pp. 1-20. DOI: 10.1016/j.jde.2003.12.005
5. Bobrowski A. Integrated Semigroups and the Trotter-Kato Theorem. Bulletin of the Polish Academy of Sciences Mathematics, 1994, vol. 41, pp. 297-304.
6. Bobrowski A. On the Yosida Approximation and the Widder-Arendt Theorem. Studia Mathematica, 1997, vol. 124, no. 3, pp. 281-290. DOI: 10.4064/sm-124-3-281-290
7. Bobrowski A. Convergence of One-Parameter Operator Semigroups. In Models of Mathematical Biology and Elsewhere. Cambridge, Cambridge University Press, 2016. DOI: 10.1017/CBO9781316480663
8. Chojnacki W. On the Equivalence of a Theorem of Kisynski and the Hille-Yosida Generation Theorem. Proceedings of the American Mathematical Society, 1998, vol. 126, no. 2, pp. 491-497. DOI: 10.1090/S0002-9939-98-04048-9
9. Chojnacki W. Multiplier Algebras, Banach Bundles, and One-Parameter Semigroups. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 1999, vol. 28, no. 2, pp. 287-322.
10. Chojnacki W. On Operator-Valued Cosine Sequences on UMD Spaces. Studia Mathematica, 2010, vol. 199, no. 3, pp. 267-278. DOI: 10.4064/sm199-3-4
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 Gunter Lumer Volume, Basel, Birkhauser, 2007, pp. 113-130. DOI: 10.1007/978-3-7643-7794-6_7
12. Cohen P.J. Factorization in Group Algebras. Duke Mathematical Journal, 1959, vol. 26, no. 2, pp. 199-205. DOI: 10.1215/S0012-7094-59-02620-1
13. Davis M.H.A. Lectures on Stochastic Control and Nonlinear Filtering. N.Y., Springer, 1984.
14. Davis M.H.A. Markov Processes and Optimization. London, Chapman and Hall, 1993.
15. Durrett R. Stochastic Calculus. A Practical Introduction. Boca Raton, CRC Press, 1996.
16. Dynkin E.B. Markov Processes. Vols. I, II. Berlin, Gottingen, Heidelberg, Springer 1965. DOI: 10.1007/978-3-662-00031-1
17. Ethier S.N., Kurtz T.G. Markov Processes. Characterization and Convergence. N.Y., Wiley, 1986. DOI: 10.1002/9780470316658
18. Elstrodt J. Mab - und Integrationstheorie. Berlin, Heidelberg, Springer, 2005. (in German) DOI: 10.1007/b137969
19. Engel K.-J., Nagel R. One-Parameter Semigroups for Linear Evolution Equations. N.Y., Springer, 2000.
20. Ermakov S.M., Nekrutkin V.V., Sipin A.S. Random Processes for Classical Equations of Mathematical Physics. Dordrecht, Kluwer Academic Publishers Group, 1989. DOI: 10.1007/978-94-009-2243-3
21. Fattorini H.O. Ordinary Differential Equations in Linear Topological Spaces. I. Journal of Differential Equations, 1969, vol. 5, pp. 72-105. DOI: 10.1016/0022-0396(69)90105-3
22. Fattorini H.O. Ordinary Differential Equations in Linear Topological Spaces. II. Journal of Differential Equations, 1969, vol. 6, pp. 50-70. DOI: 10.1016/0022-0396(69)90117-X
23. Fattorini H.O. Second Order Linear Differential Equations in Banach Spaces. Amsterdam, North-Holland, 1985.
24. Freidlin M. Functional Integration and Partial Differential Equations. Princeton, Princeton University Press, 1985.
25. Goldstein S. On Diffusion by Discontinuous Movements, and on the Telegraph Equation. The Quarterly Journal of Mechanics and Applied Mathematics, 1951, no. 4, pp. 129-156.
26. Goldstein J.A. Semigroups of Linear Operators and Applications. N.Y., Oxford University Press, 1985.
27. Haase M. The Group Reduction for Bounded Cosine Functions on UMD Spaces. Mathematische Zeitschrift, 2009, vol. 262, no. 2, pp. 281-299. DOI: 10.1007/s00209-008-0373-y
28. Heyer H.Probability Measures on Locally Compact Groups. Berlin, Heidelberg, Springer, 1977. DOI: 10.1007/978-3-642-66706-0
29. Hille E. Functional Analysis and Semi-Groups. N.Y., American Mathematical Society, 1948.
30. Hennig B., Neubrander F. On Representations, Inversions and Approximations of Laplace Transform in Banach Spaces. Applicable Analysis, 1993, vol. 49, pp. 151-170.
31. Hewitt E., Ross K.A. Abstract Harmonic Analysis. Vol. II: Structure and Analysis for Compact Groups. Analysis on Locally Compact Abelian Groups. Berlin, Heidelberg, Springer, 1970. DOI: 10.1007/978-3-662-26755-4
32. Janssen A., Siebert E. Convolution Semigroups and Generalized Telegraph Equations. Mathematische Zeitschrift, 1981, vol. 177, no. 4, pp. 519-532. DOI: 10.1007/BF01219084
33. Kac M. Some Stochastic Problems in Physics and Mechanics. Colloq. Lect. 2, Magnolia Petrolum, 1956.
34. Kisynski J. Sur la methode des approximations successives pour un systeme de n equations a n inconnues. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys., 1958, vol. 6, pp. 683-687. (in French)
35. Kisynski J. Sur les equations differentielles dans les espaces de Banach. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys., 1959, vol. 7, pp. 381-385. (in French)
36. Kisynski J. Convergence du type L. Colloquium Mathematicum, 1959/1960, vol. 7, pp. 205-211. (in French) DOI: 10.4064/cm-7-2-205-211
37. Kisynski J. Sur les familles compactes de fonctions mesurables. Colloquium Mathematicum, 1959/1960, vol. 7, pp. 221-235. (in French) DOI: 10.4064/cm-7-2-221-235
38. Kisynski J. Sur les operateurs de Green des problemes de Cauchy abstraits. Studia Mathematica, 1963/1964, vol. 23, pp. 285-328. (in French) DOI: 10.4064/sm-23-3-285-328
39. Kisynski J. On Temporally Inhomogeneous Equations of Evolution in Banach Spaces. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys., 1966, vol. 14, pp. 623-626.
40. Kisynski J. A Proof of the Trotter-Kato Theorem on Approximation of Semigroups. Colloquium Mathematicum, 1967, vol. 18, pp. 181-184. DOI: 10.4064/cm-18-1-181-184
41. Kisynski J. On the Generation of Tight Measures. Studia Mathematica, 1968, vol. 30, pp. 141-151. DOI: 10.4064/sm-30-2-141-151
42. Kisynski J. On Second Order Cauchy's Problem in a Banach Space. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys., 1970, vol. 18, no. 7, pp. 371-374.
43. Kisynski J. On Operator-Valued Solutions of d'Alembert's Functional Equation. I. Colloquium Mathematicum, 1971, vol. 23, pp. 107-114. DOI: 10.4064/cm-23-1-107-114
44. Kisynski J. On Cosine Operator Functions and One-Parameter Groups of Operators. Studia Mathematica, 1972, vol. 44, pp. 93-105. DOI: 10.4064/sm-44-1-93-105
45. Kisynski J. On Operator-Valued Solutions of d'Alembert's Functional Equation. II. Studia Mathematica, 1972, vol. 42, pp. 43-66.
46. Kisynski J. On M. Kac's Probabilistic Formula for the Solutions of the Telegraphist's Equation. Annales Polonici Mathematici, 1974, vol. 29, pp. 259-272. DOI: 10.4064/ap-29-3-259-272
47. Kisynski 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), Vienna, International Atomic Energy Agency, 1976, vol. 3, pp. 305-405.
48. Kisynski J. The Argument of a Lagrange Subspace and the Maslov Index. Institute of Mathematics, Polish Academy of Sciences, Preprint 202, 1979.
49. Kisy'nski J. On Semigroups Generated by Differential Operators on Lie Groups. Journal of Functional Analysis, 1979, vol. 31, no. 2, pp. 234-244. DOI: 10.1016/0022-1236(79)90064-8
50. Kisynski J. O rownaniu telegrafistow z malym parametrem [On the Telegraph Equation with a Small Parameter]. Prace Naukowe Politechniki Lubelskiej 212, Matematyka [Research Bulletin of Lublin University of Technology], 1991, vol. 12, pp. 14-27. (in Polish)
51. Kisynski J. The Widder Spaces, Representations of the Convolution Algebra L^1(R^+) and One Parameter Semigroups of Operators. Institute of Mathematics, Polish Academy of Sciences, 1998, Preprint 588, pp. 1-36.
52. Kisynski J. On Cohen's Proof of the Factorization Theorem. Annales Polonici Mathematici, 2000, vol. 75, no. 2, pp. 177-192. DOI: 10.4064/ap-75-2-177-192
53. Kisynski J. On Fourier Transforms of Distribution Semigroups. Journal of Functional Analysis, 2007, vol. 242, pp. 400-441. DOI: 10.1016/j.jfa.2006.07.003
54. Kolmogorov A.N. Uber die analytischen Methoden in der Wahrscheinlichkeitsrechnung. Mathematische Annalen, 1931, vol. 104, no. 1, pp. 415-458. (in German) DOI: 10.1007/BF01457949
55. Kolesnik A.D. The Explicit Probability Distribution of the Sum of Two Telegraph Processes. Stochastics and Dynamics, 2015, vol. 15, no. 2, article ID: 1550013, 32 p.
56. Krein S.G. Linear Differential Equations in Banach Space. Providence, American Mathematical Society, 1971.
57. Lions J.-L. Equations differentielles operationnelles et problemes aux limites. Die Grundlehren der mathematischen Wissenschaften, Berlin, Gottingen, Heidelberg, Springer, 1961. (in French)
58. Lax P.D., Phillips R.S. Scattering Theory. N.Y., Academic Press, 1967.
59. Natanson I.P. Teoriya funkciy veshchestvennoy peremennoy [Theory of Functions of Real Variable]. Moscow, Gosudarstvennoe izdatel'stvo tekhnichesko-teoreticheskoy literatury, 1957. (in Russian)
60. Da Prato G., Giusti F. Una carracterizzazione dei generatori di funzioni coseno astratte. Bollettino dell'Unione Matematica Italiana, 1967, vol. 22, pp. 357-362. (in Italian)
61. Pinsky M.A. Lectures on Random Evolutions. Singapore, World Scientific, 1991. DOI: 10.1142/1328
62. Rudnicki R., Tyran-Kaminska M. Piecewise Deterministic Processes in Biological Models. Springer International Publishing, 2017. DOI: 10.1007/978-3-319-61295-9
63. Simon B. Quantum Mechanics for Hamiltonians Defined as Quadratic Forms. Princeton, Princeton University Press, 1971.
64. Sova M. Cosine Operator Functions. Rozprawy Matematyczne, 1966, vol. 49, pp. 1-47.
65. Wentzell A.D. A Course in the Theory of Stochastic Processes. N.Y., McGraw-Hill International Book, 1981.
66. Yosida K. Functional Analysis. Berlin, Springer, 1965.