Matematyczny dorobek Pawła Domańskiego

• Autorzy: Bonet J. , Langenbruch M.
• Języki publikacji: PL

Abstrakty

PL

Paweł Domański był wspaniałym matematykiem, darzonym powszechnym szacunkiem w międzynarodowym środowisku matematycznym. Miał szerokie zainteresowania i rozległą wiedzę w wielu powiązanych ze sobą działach matematyki, szczególnie w analizie matematycznej, analizie funkcjonalnej, przestrzeniach Banacha, algebrach topologicznych, algebrze homologicznej, analizie zespolonej jednej i wielu zmiennych, równaniach różniczkowych cząstkowych oraz innych. Był dobrym wykładowcą, czytelnie przedstawiał swoje pomysły w pracach badawczych i przeglądowych. Artykuł zawiera biografię uczonego, analizę wielu jego dokonań, spis prac i listę uczniów.

Słowa kluczowe

PL

matematycy polscy; Paweł Domański; operatory kompozycji; funkcje holomorficzne; algebry topologiczne

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2017
• Tom: T. 53, Nr 1
• Strony: 1--41
• Opis fizyczny: Bibliogr. 69 poz., fot.

Twórcy

autor

Bonet J.

• Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politécnica de València

autor

Langenbruch M.

• Department of Mathematics, University Oldenburg

Bibliografia

• [1] S. A. Argyros, R. G. Haydon, A hereditarily indecomposable ℒ∞-space that solves the scalar-plus-compact problem, Acta Math. 206 (2011), nr 1,1-54.
• [2] R.-L. Arikan, H. and V. Zahariuta, Holomorphic functional calculus for operators on a locally convex space, Results Math. 43 (2003), 23-36.
• [3] S. Banach, Teorja operacyj, tom I. Operacje liniowe, Wydawnictwo Kasy im. Mianowskiego, Warszawa 1931.
• [4] F. Bayart, É Matheron, Dynamics of linear operators, Cambridge Tracts in Mathematics, t. 179, Cambridge University Press, Cambridge 2009.
• [5] K. D. Bierstedt, J. Bonet, Some aspects of the modern theory of Fréchet spaces, RACSAM. Rev. R. Acad. Cienc. Exactas Fi s. Nat. Ser. A Mat. 97 (2003), nr 2, 159-188.
• [6] E. Bierstone, P. D. Milman, Composite differentiable functions, Math. Ann. 116 (1982), 541-558.
• [7] P. D. Milman, E. Bierstone, W. Pawłucki, Composite differentiable functions, Duke Math. J. 83 (1996), 607-620.
• [8] F. E. Browder, Analyticity and partial differential equations. I, Amer. J. Math. 84 (1962), 666-710.
• [9] R. Brück, J. Müller, Invertible elements in a convolution algebra of holomorphic functions, Math. Ann. 94 (1992), 421-438.
• [10] R. Brück, H. Render, Invertibility of holomorphic functions with respect to the Hadamard product, Complex Variables 42 (2000), 207-223.
• [11] A. Chigogidze, Complemented subspaces of products of Banach spaces, Proc. Amer. Math. Soc. 129 (2001), nr 10, 2959-2963.
• [12] O.-J. G. Sokal, A. D. Y. Choe, D. G. Wagner, Homogeneous multivariate polynomials with the half-plane property, Advances in Appl. Math. 32 (2004), 88-187.
• [13] C. Cowen, B. MacCluer, Composition operators on spaces of analytic functions, CRC Press, Boca Raton 1995.
• [14] C. C. Cowen, B. D. MacCluer, Composition operators on spaces of analytic functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL 1995.
• [15] W. J. Davis, T. Figiel, W. B. Johnson, A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327.
• [16] L. Drewnowski, Copies of l∞ in an operator space, Math. Proc. Cambridge Philos. Soc. 108 (1990), nr 3, 523-526.
• [17] K.-J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, t. 194, Springer, New York 2000.
• [18] L. Frerick, J. Wengenroth, (LB)-spaces of vector-valued continuous functions, Bull. Lond. Math. Soc. 40 (2008), nr 3, 505-515.
• [19] L. Frerick, J. Wengenroth, The mathematical work of Susanne Dierolf Funct. Approx. Comment. Math. 44 (2011), nr 1, 7-31.
• [20] G. Glaeser, Fonctions composées différentiables, Math. Ann. 77 (1963), 193-209.
• [21] W. T. Gowers, B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), nr 4, 851-874.
• [22] K.-G. Grosse-Erdmann, A. P. Manguillot, Linear chaos, Springer, London 2011.
• [23] J. Hadamard, Essai sur l’etude des fonctions données pour leurs développements de Taylor, J. de Mathématique 8 (1982), nr 4, 101-186.
• [24] L. Hörmander, The analysis of linear partial differential operators, I, II, Springer. Berlin 1983.
• [25] P. D. F. Ion, T. Kawai, Theory of vector-valued hyperfunctions, Publ. Res. Inst. Math. Sci. 11 (1975/76), nr 1, 1-19.
• [26] R. Ishimura, Existence locale de solutions holomorphes pour les équations différentielles d’ordre infini, Ann. Inst. Fourier 35 (1985), 49-57.
• [27] R. Ishimura, Sur les équations différentielles d’ordre infini d’Euler, Mem. Fac. Sci. Kyushu Univ. Ser. A 44 (1990), nr 1, 1-10.
• [28] Y. Ito, Fourier hyperfuction semigroups, J. Math. Tokushima Univ. 16 (1982), 33-53.
• [29] T. Kalmes, Some results on P-convexity and the problem of parameter dependence for solutions of linear partial differential equations, dostępne pod adresem https://arxiv.org/abs/1408.4356.
• [30] T. Kalmes, The augmented operator of a surjective partial differential operator with constant coefficients need not be surjective, Bull. London Math. Soc. 44 (2012), 610-614.
• [31] T. Kalmes, Some results on surjectivity of augmented differential operators, J. Math. Anal. Appl. 386 (2012), 125-134.
• [32] N. J. Kalton, The basic sequence problem, Studia Math. 116 (1995), nr 2, 167-187.
• [33] N. J. Kalton, A. Pełczyński, Kernels of surjections from L1-spaces with an application to Sidon sets, Math. Ann. 309 (1997), nr 1, 135-158.
• [34] J. Kisyński, Distribution semigroups and one parameter semigroups, Bull. Pol. Acad. Sci. Math. 50 (2002), 189-216.
• [35] J. Kisyński, On Fourier transforms of distribution semigroups, J. Funct. Anal. 242 (2007), 400-441.
• [36] H. Komatsu, Semigroups of operators in locally convex spaces, J. Math. Soc. Japan 16 (1964), 230-262.
• [37] U. Krengel, Ergodic theorems, de Gruyter Studies in Mathematics, t. 6, Walter de Gruyter & Co., Berlin 1985.
• [38] K. Kruse, Vector valued Fourier hyperfunctions, praca doktorska, Oldenburg 2014.
• [39] P. Ch. Kunstmann, Distribution semigroups and abstract Cauchy problems, Trans. Amer. Math. Soc. 351 (1999), 837-856.
• [40] M. Langenbruch, Continuous linear right inverses for convolution operators in spaces of real analytic functions, Studia Math. 110 (1994), 65-82.
• [41] W. Lusky, On the isomorphism classes of weighted spaces of harmonic and holomorphic functions, Studia Math. 175 (2006), nr 1, 19-45.
• [42] F. Mantlik, Partial differential operators depending analytically on a parameter, Ann. Inst. Fourier (Grenoble) 41 (1991), 577-599.
• [43] F. Mantlik, Fundamental solutions for hypoelliptic differential operators depending analytically on a parameter, Trans. Amer. Math. Soc. 334 (1992), 245-257.
• [44] R. Meise, B. A. Taylor, D. Vogt, Characterization of the linear partial differential operators with constant coefficients admitting a continuous linear right inverse, Ann. Inst. Fourier (Grenoble) 40 (1990), 619-655.
• [45] R. Meise, D. Vogt, Introduction to functional analysis, t. 2, Clarendon Press, Oxford University Press, New York 1997.
• [46] I. V. Melnikova, A. Filinkov, Abstract Cauchy problems three approaches, Monographs and Surveys in Pure Appl. Math., t. 120, Chapman & Hall, Boca Raton 2001.
• [47] G. Metafune, V. B. Moscatelli, Quojection and prequojections, Advances in the theory of Fréchet spaces (Istanbul, 1988), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., t. 287, Kluwer Acad. Publ., Dordrecht 1989, 235-254.
• [48] M. I. Ostrovskiĭ, On complemented subspaces of sums and products of Banach spaces, Proc. Amer. Math. Soc. 124 (1996), nr 7, 2005-2012.
• [49] S. Ōuchi, Semi-groups of operators in locally convex spaces, J. Math. Soc. Japan 29 (1973), 265-276.
• [50] V. P. Palamodov, On a Stein manifold the Dolbeault complex splits in positive dimensions, Math.USSR Sbornik 17 (1972), 289-315.
• [51] V. P. Palamodov, A criterion for splitness of differential complexes with constant coefficients, [w:] Geometrical and aalgebraical aspects in several variables (C. A. Berenstein, D. Struppa, red.), EdtEl 1991, 265-291.
• [52] H. Render, Hadamard’s multiplication theorem - recent developments, Colloquium Math. 74 (1997), 79-92.
• [53] M. Sato, Theory of hyperfunctions, J. Fac. Sci. Univ. Tokyo, Sec. I 8 (1959/60), 139-193.
• [54] K. Seip, Beurling type density theorems in the unit disk, Invent. Math. 113 (1993), nr 1, 21-39.
• [55] J. H. Shapiro, Composition operators and classical function theory, Springer, New York 1993.
• [56] J. C. Tougeron, Fonctions composées différentiables, Ann. Inst. Fourier (Grenoble) 30 (1980), nr 4, 51-74.
• [57] F. Trêves, Fundamental solutions of linear partial differential equations with constant coefficients depending on parameters, Bull. Soc. Math. France 90 (1962), 473-486.
• [58] F. Trêves, Un théorème sur les équations aux dérivées partielles à coefficients constants dépendant de paramètres, Amer. J. Math. 84 (1962), 561-577.
• [59] D. Vogt, A division theorem for real analytic functions, Bull. Lond. Math. Soc. 39 (2007), nr 5, 818-828.
• [60] D. Vogt, Extension operators for real analytic functions on compact subvarieties on Rd, J. Reine Angew. Math. 606 (2007), 217-233.
• [61] D. Vogt, A nuclear Fréchet space consisting of C°° -functions and failing the bounded approximation property, Proc. Amer. Math. Soc. 138 (2010), nr 4, 1421-1423.
• [62] D. Vogt, Hadamard operators on D1(Rd), Studia Math. 237 (2017), 137-152.
• [63] D. Vogt, Hadamard operators on D1(Ω), Math. Nachr. 290 (2017), 1374-1380.
• [64] D. Vogt, On the functors Ext1 (E, F) for Fréchet spaces, Studia Math. 85 (1987), nr 2, 163-197.
• [65] D. Vogt, ℇ1 as an algebra by multiplicative convolution (2015), dostępne pod adresem https://arxiv.org/abs/1509.05759.
• [66] D. Vogt, Operators of Hadamard type on spaces of smooth functions, Math. Nachr. 288 (2015), 353-361.
• [67] S. Wang Wang, Quasi-distribution semigroups and integrated semigroups, J. Funct. Anal. 146 (1997). 352-381.
• [68] J. Wengenroth, A splitting theorem for subspaces and quotients of D’, Bull. Pol. Acad. Sci., Math. 49 (2001), nr 4, 349-354.
• [69] J. Wengenroth, Derived functors in functional analysis, Lecture Notes in Mathematics, t. 1810, Springer-Verlag, Berlin 2003.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).