Bogdan Ziemian (1953-1997)

• Autorzy: Bogdan Bojarski , Stanisław Łojasiewicz , Grzegorz Łysik , Zofia Szmydt
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 74
• Numer: 1
• Strony: 1-11

Twórcy

autor

Bogdan Bojarski

• Warszawa, Polska

autor

Stanisław Łojasiewicz

• Kraków, Polska

autor

Grzegorz Łysik

• Warszawa, Polska

autor

Zofia Szmydt

• Warszawa, Polska

Bibliografia

• [1] The group G of proper Lorentz transformations and G-invariant distributions, Appendix in: Z. Szmydt, Fourier Transformations and Linear Differential Equations, PWN, Warszawa, and Reidel, Dordrecht, 1977, 464-471.
• [2] On distributions invariant with respect to some linear transformations, Ann. Polon. Math. 36 (1979), 261-276.
• [3] Fundamental solution $E_n$ of the operator $∂^2/∂t^2 - Δ_n$ for n ≥ 3 (with Z. Szmydt), %Ann. Polon. Math. 36 (1979), ibid., 277-286.
• [4] On G-invariant distributions, J. Differential Equations 35 (1980), 66-86.
• [5] Special solutions of the equations Pu = 0, Pu = δ for invariant linear differential operators with polynomial coefficients (with Z. Szmydt), J. Differential Equations 39 (1981), 226-256.
• [6] Distributions invariant under compact Lie groups, Ann. Polon. Math. 42 (1983), 175-183.
• [7] Fundamental solution for operators preserving a quadratic form (with Z. Szmydt), ibid., 369-386.
• [8] A method for constructing invariant fundamental solutions for invariant operators (with Z. Szmydt), in: Proc. Conf. Convergence and Generalized Functions (Kato- wice, 1983), IM PAN, Warszawa, 1984, 149-155.
• [9] A method for constructing invariant fundamental solutions for $P(Δ_m)$ (with Z. Szmydt), Zeszyty Naukowe Politechniki Śląskiej Ser. Mat.-Fiz. 48 (1986), 147-164.
• [10] Explicit invariant solutions for invariant linear differential operators (with Z. Szmydt), Proc. Roy. Soc. Edinburgh 98 (1984), 149-166.
• [11] Local order function for homogeneous rotation invariant distributions and their multiplication (with Z. Szmydt), Ann. Univ. Mariae Curie-Skłodowska Sect. A 38 (1984), 139-143.
• [12] A Taylor type decomposition for distributions in one dimension, Bull. Polish Acad. Sci. Math. 32 (1984), 143-155.
• [13] An analysis of microlocal singularities of functions and distributions on the real line, ibid., 157-164.
• [14] The derivative of a measurable function and of a distribution at a point and its basic properties, ibid., 165-177.
• [15] An invariance method for constructing fundamental solutions for $P(□_mn)$ (with Z. Szmydt), Ann. Polon. Math. 46 (1985), 333-360.
• [16] Singular ordinary differential equations on spaces of singular test functions with applications to invariant partial differential operators (with Z. Szmydt), in: Proc. Conf. Differential Equations and Applications (Rousse, 1985), 1987, 955-958.
• [17] The Mellin transformation and microlocal singularities of distributions, %Proc. Conf. Diff. Equ. Appl. Rousse 1985, (1987), ibid., 1005-1008.
• [18] Invariant fundamental solution of the wave operator (with Z. Szmydt), Demonstratio Math. 19 (1986), 371-386.
• [19] Taylor formula for distributions in several dimensions, Bull. Polish Acad. Sci. Math. 34 (1986), 277-286.
• [20] Multidimensional Mellin transformation and partial differential operators with regular singularity (with Z. Szmydt), ibid. 35 (1987), 167-180.
• [21] Mellin analysis of singularities (with G. Łysik), in: Proc. Internat. Summer School on Nonlinear Differential Equations (Varna, 1987).
• [22] Solutions of singular elliptic equations via the Mellin transformation on sets of high order of tangency to the singular lines (with Z. Szmydt), Bull. Polish Acad. Sci. Math. 36 (1988), 521-535.
• [23] Taylor formula for distributions, Dissertationes Math. (Rozprawy Mat.) 264 (1988)
• [24] The Mellin transformation and multidimensional generalized Taylor expansions of singular functions, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (1989), 263-295.
• [25] Local existence and regularity of solutions of singular elliptic operators on manifolds with corner singularities (with Z. Szmydt), J. Differential Equations 83 (1990), 1-25.
• [26] Mean value theorems for linear and semi-linear rotation invariant operators, Ann. Polon. Math. 51 (1990), 341-348.
• [27] Generalized Taylor expansions and theory of resurgent functions of Jean Ecalle, in: Proc. Conf. Generalized Functions and Convergence (Katowice, 1988), World Sci., 1990, 285-295.
• [28] Second microlocalization and the Mellin transformation (with H. Kołakowski), Publ. Res. Inst. Math. Sci. % Kyoto University, 26 (1990), 785-801.
• [29] Continuous radial asymptotics for solutions to elliptic Fuchsian equations in 2-dimensions, in: Proc. Sympos. Microlocal Analysis and Its Applications (Kyoto, 1990), Sûrikaisekikenkyûsho Kôkyûroku 750, Kyoto, 1991, 3-19.
• [30] The modified Cauchy transformation with applications to generalized Taylor expansions, Studia Math. 102 (1992), 1-24.
• [31] Characterization of Mellin distributions supported by certain noncompact sets (with Z. Szmydt), ibid., 25-38.
• [32] Elliptic corner operators in spaces with continuous radial asymptotics I, J. Differential Equations 101 (1993), 28-57.
• [33] Elliptic corner operators in spaces with continuous radial asymptotics II, in: Partial Differential Equations, Banach Center Publ. 27, IM PAN, Warszawa, 1992, 555-580.
• [34] The Mellin Transformation and Fuchsian Type Partial Differential Equations (with Z. Szmydt), Math. Appl. 56, Kluwer, Dordrecht, 1992.
• [35] Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293.
• [36] Mellin analysis of singular and non-linear PDEs, in: Proc. Conf. Equadiff 8 (Bratislava, 1993), Tatra Mt. Math. Publ. 4 (1994), 243-248.
• [37] Exact radial asymptotics of solutions to singular elliptic differential equations (with G. Łysik), in: Proc. Fifth Internat. Colloquium on Differential Equations (Plovdiv, 1994), VSP, Utrecht, 1995, 213-221.
• [38] Between the Paley-Wiener theorem and the Bochner tube theorem (with Z. Szmydt), Ann. Polon. Math. 60 (1995), 299-304.
• [39] Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. (Rozprawy Mat.) 354 (1996).
• [40] A remark on Nilsson type integrals (with Nguyen Si Minh), in: Singularities and Differential Equations, Banach Center Publ. 33, IM PAN, Warszawa, 1996, 277-285.
• [41] Uogólnione funkcje analityczne z zastosowaniami [Generalized analytic functions with applications] (with G. Łysik), Wiadom. Mat. 32 (1996), 15-25 (in Polish).
• [42] Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables (with M. E. Pliś), Ann. Polon. Math. 67 (1997), 31-41.
• [43] Laplace distributions and hyperfunctions on $\overline{ℝ}^{n}_{+}$ (with Z. Szmydt), J. Math. Sci. Tokyo Univ. 5 (1998), 41-74.
• [44] Topological imbedding of Laplace distributions in Laplace hyperfunctions (with Z. Szmydt), Dissertationes Math. (Rozprawy Mat.) 376 (1998).
• [45] Convolution equations in the space of Laplace distributions (with M. E. Pliś), Ann. Polon. Math. 69 (1998), 271-181.
• [46] On extendability of invariant distributions, posthumous, this volume, 13-25. Bogdan Ziemian's preprints
• [P1] 20 lectures on ordinary and partial differential equations. Geometric methods of complex analysis, preprint, IM PAN, Warszawa, 1992.
• [P2] Holomorphic regularization of meromorphic functions, preprint, Université de Tours, 1996.
• [P3] Unfinished notes of Bogdan Ziemian, preprint, IM PAN, Warszawa, 2000. Other references
• [R1] H. Kołakowski, Mellin analysis of partial differential equations in papers of B. Ziemian, this volume, 27-33.
• [R2] G. Łysik, Generalized analytic functions of Bogdan Ziemian, this volume, 35-41.
• [R3] G. Łysik, Laplace integrals in partial differential equations in papers of Bogdan Ziemian, this volume, 43-50.