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The occasion for this survey article was the 70th birthday of Jan Stochel, professor at Jagiellonian University, former head of the Chair of Functional Analysis and a prominent member of the Kraków school of operator theory. In the course of his mathematical career, he has dealt, among other things, with various aspects of functional analysis, single and multivariable operator theory, the theory of moments, the theory of orthogonal polynomials, the theory of reproducing kernel Hilbert spaces, and mathematical aspects of quantum mechanics.
Czasopismo
Rocznik
Tom
Strony
303--321
Opis fizyczny
Bibliogr. 63 poz., rys.
Twórcy
autor
- Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, 208016, India
autor
- University of Iowa, Iowa City, Iowa 52242, USA
autor
- Instytut Matematyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, 30-348 Kraków, Poland
autor
- Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea
autor
- Department of Mathematics, University of California at Santa Barbara, Santa Barbara, CA 93106-3080, USA
- School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK
Bibliografia
- [1] J. Agler, M. Stankus, m-isometric transformations of Hilbert spaces, I, Integral Equations Operator Theory 21 (1995), 383–429.
- [2] J. Agler, M. Stankus, m-isometric transformations of Hilbert spaces, II, Integral Equations Operator Theory 23 (1995), 1–48.
- [3] J. Agler, M. Stankus, m-isometric transformations of Hilbert spaces, III, Integral Equations Operator Theory 24 (1996), 379–421.
- [4] A. Anand, S. Chavan, Z.J. Jabłoński, J. Stochel, A solution to the Cauchy dual subnormality problem for 2-isometries, J. Funct. Anal. 277 (2019), no. 12, Article no. 108292.
- [5] A. Anand, S. Chavan, Z.J. Jabłoński, J. Stochel, The Cauchy dual subnormality problem for cyclic 2-isometries, Adv. Oper. Theory 5 (2020), 1061–1077.
- [6] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404.
- [7] A. Athavale, On completely hyperexpansive operators, Proc. Amer. Math. Soc. 124 (1996), 3745–3752.
- [8] A. Athavale, S. Chavan, Sectorial forms and unbounded subnormals, Math. Proc. Cambridge Philos. Soc. 143 (2007), no. 3, 685–702.
- [9] C. Badea, L. Suciu, The Cauchy dual and 2-isometric liftings of concave operators, J. Math. Anal. Appl. 472 (2019), 1458–1474.
- [10] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961), 187–214.
- [11] C.A. Berger, L.A. Coburn, Toeplitz operators and quantum mechanics, J. Funct. Anal. 68 (1986), 273–299.
- [12] P. Budzyński, Z. Jabłoński, I.B. Jung, J. Stochel, Unbounded subnormal weighted shifts on directed trees, J. Math. Anal. Appl. 394 (2012), 819–834.
- [13] P. Budzyński, Z. Jabłoński, I.B. Jung, J. Stochel, Unbounded subnormal weighted shifts on directed trees. II, J. Math. Anal. Appl. 398 (2013), 600–608.
- [14] P. Budzyński, Z.J. Jabłoński, I.B. Jung, J. Stochel, Unbounded subnormal composition operators in L2-spaces, J. Funct. Anal. 269 (2015), 2110–2164.
- [15] P. Budzyński, Z. Jabłoński, I.B. Jung, J. Stochel, A subnormal weighted shift on a directed tree whose nth power has trivial domain, J. Math. Anal. Appl. 435 (2016), 302–314.
- [16] P. Budzyński, Z.J. Jabloński, I.B. Jung, J. Stochel, Subnormality of unbounded composition operators over one-circuit directed graphs: exotic examples, Adv. Math. 310 (2017), 484–556.
- [17] P. Budzyński, Z. Jabłoński, I.B. Jung, J. Stochel, Unbounded Weighted Composition Operators in L2-Spaces, Lecture Notes in Math., vol. 2209, Springer, 2018.
- [18] S. Chavan, A spectral exclusion principle for unbounded subnormals, Proc. Amer. Math. Soc. 137 (2009), 211–218.
- [19] S. Chavan, An inequality for spherical Cauchy dual tuples, Colloq. Math. 131 (2013), 265–272.
- [20] S. Chavan, D.K. Pradhan, S. Trivedi, Multishifts on directed Cartesian products of rooted directed trees, Dissertationes Math. 527 (2017), 102 pp.
- [21] S. Chavan, Z.J. Jabłoński, I.B. Jung, J. Stochel, Taylor spectrum approach to Brownian-type operators with quasinormal entry, Ann. Mat. Pur. Appl. 200 (2021), 881–922.
- [22] P. Chernoff, A semibounded closed symmetric operator whose square has trivial domain, Proc. Amer. Math. Soc. 89 (1983), 289–290.
- [23] D. Cichoń, J. Stochel, F. Szafraniec, Extending positive definiteness, Trans. Amer. Math. Soc. 363 (2011), 545–577.
- [24] J.B. Conway, The Theory of Subnormal Operators, Mathematical Surveys and Monographs, vol. 36, Providence, RI: American Mathematical Society, 1991.
- [25] R.E. Curto, Featured Review of Solving moment problems by dimensional extension, by M. Putinar and F.-H. Vasilescu, Annals of Math. 149 (1999), 1087–1107, and The complex moment problem and subnormality: A polar decomposition approach, by J. Stochel and F. Szafraniec, J. Funct. Anal. 159 (1998), 432–491, Math. Rev.
- [26] G. Exner, I.B. Jung, J. Stochel, H.Y. Yun, A subnormal completion problem for weighted shifts on directed trees, Integral Equations Operator Theory 90 (2018), Article no. 72.
- [27] G. Exner, I.B. Jung, J. Stochel, H.Y. Yun, A subnormal completion problem for weighted shifts on directed trees, II, Integral Equations Operator Theory 92 (2020), Article no. 8.
- [28] G.P. Gehér, Asymptotic behaviour and cyclic properties of weighted shifts on directed trees, J. Math. Anal. Appl. 440 (2016), no. 1, 14–32.
- [29] P. Gérard, A Pushnitski, Unbounded Hankel operators and the flow of the cubic Szegö equation, Invent. Math. 232 (2023), 995–1026.
- [30] P.R. Halmos, Normal dilations and extensions of operators, Summa Brasil. Math. 2 (1950), 125–134.
- [31] P.R. Halmos, A Hilbert Space Problem Book, second edition, Grad. Texts in Math., vol. 19, Springer-Verlag, New York, Berlin, 1982.
- [32] Z. Jabłoński, I.B. Jung, J. Stochel, Weighted shifts on directed trees, Mem. Amer. Math. Soc. 216 (2012), no. 1017.
- [33] Z.J. Jabłoński, I.B. Jung, J. Stochel, A non-hyponormal operator generating Stieltjes moment sequences, J. Funct. Anal. 262 (2012), 3946–3980.
- [34] Z. Jabłoński, I.B. Jung, J. Stochel, Normal extensions escape from the class of weighted shifts on directed trees, Complex Anal. Oper. Theory 7 (2013), 409–419.
- [35] Z. Jabłoński, I.B. Jung, J. Stochel, Operators with absolute continuity properties: an application to quasinormality, Studia Math. 215 (2013), 11–30.
- [36] Z. Jabłoński, I.B. Jung, J. Stochel, A hyponormal weighted shift on a directed tree whose square has trivial domain, Proc. Amer. Math. Soc. 142 (2014), 3109–3116.
- [37] Z. Jabłoński, I.B. Jung, J. Stochel, Unbounded quasinormal operators revisited, Integral Equations Operator Theory 79 (2014), 135–149.
- [38] A. Lambert, Subnormality and weighted shifts, J. Lond. Math. Soc. (2) 14 (1976), 476–480.
- [39] A. Lambert, Subnormal composition operators, Proc. Amer. Math. Soc. 103 (1988), 750–754.
- [40] A. Lambert, Normal extensions of subnormal composition operators, Michigan Math. J. 35 (1988), 443–450.
- [41] H.J. Landau, Classical background of the moment problem, Proc. Sympos. Appl. Math. 37 (1987), 1–15.
- [42] W. Majdak, J.B. Stochel, Weighted shifts on directed semi-trees: an application to creation operators on Segal–Bargmann spaces, Complex Anal. Oper. Theory 10 (2016), no. 7, 1427–1452.
- [43] M. Naimark, On the square of a closed symmetric operator, Dokl. Akad. Nauk SSSR 26 (1940), 866–870.
- [44] M. Naimark, On the square of a closed symmetric operator, Dokl. Akad. Nauk SSSR 28 (1940), 207–208.
- [45] E. Nordgren, Composition operators on Hilbert spaces, Lecture Notes in Math., vol. 693, Springer-Verlag, Berlin, 1978, 37–63.
- [46] S.K. Parrott, Weighted translation operators, Ph.D. Thesis, Univ. of Michigan, 1965.
- [47] M. Putinar, F.H. Vasilescu, Solving moment problems by dimensional extension, Ann. of Math. (2) 149 (1999), 1087–1107.
- [48] M. Reed, B. Simon, Methods of Modern Mathematical Physics, vol. II, Academic Press, San Diego, 1975.
- [49] R. Schilling, R. Song, Z. Vondracek, Bernstein Functions: Theory and Applications, Berlin, Boston: De Gruyter, 2012.
- [50] K. Schmüdgen, On domains of powers of closed symmetric operators, J. Operator Theory 9 (1983), 53–75.
- [51] I.E. Segal, Mathematical problems of relativistic physics, Chapter 4 [in:] M. Kac (ed.), Proceedings of the Summer Seminar, Boulder, Colorado 1960, vol. II; Lectures in Applied Mathematics, AMS, Providence, RI, 1963.
- [52] S. Shimorin, Wold-type decompositions and wandering subspaces for operators close to isometries, J. Reine Angew. Math. 531 (2001), 147–189.
- [53] S. Shimorin, Complete Nevanlinna–Pick property of Dirichlet-type spaces, J. Funct. Anal. 191 (2002), 276–296.
- [54] B. Simon, The classical moment problem as a self-adjoint finite difference operator, Adv. Math. 137 (1998), 82–203.
- [55] T. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Univ. Toulouse 8 (1894), J1-J122.
- [56] T. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Univ. Toulouse 9 (1895), A5-A47.
- [57] J. Stochel, F.H. Szafraniec, On normal extensions of unbounded operators. I, J. Operator Theory 14 (1985), 31–55.
- [58] J. Stochel, F.H. Szafraniec, On normal extensions of unbounded operators. II, Acta Sci. Math. (Szeged) 53 (1989), 153–177.
- [59] J. Stochel, F.H. Szafraniec, On normal extensions of unbounded operators. III: Spectral properties, Publ. Res. Inst. Math. Sci. 25 (1989), 105–139.
- [60] J. Stochel, F.H. Szafraniec, Unbounded weighted shifts and subnormality, Integral Equations Operator Theory 12 (1989), 145–153.
- [61] J. Stochel, F.H. Szafraniec, Algebraic operators and moments on algebraic sets, Port. Math. 51 (1994), 25–45.
- [62] J. Stochel, F.H. Szafraniec, The complex moment problem and subnormality: a polar decomposition approach, J. Funct. Anal. 159 (1998), 432–491.
- [63] J. Stochel, F.H. Szafraniec, A peculiarity of the creation operator, Glasg. Math. J. 44 (2002), 137–147.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e9fe8a5e-0370-43dc-9964-4a558e3dc215