Ilie Valusescu

Academic Rank:

Senior Researcher

Department:

Operator Theory and Functional Analysis

Current Research Interests:

• Functional Analysis
• Harmonic Analysis
• Spectral Theory
• Operator Theory
• Prediction and Filtering Theory
• Mathematical Theory of Systems and Networks

Short presentation of scientifical activity:

• Faculty of Mathematics, graduated 1970. Disertation on Analytic discs in comutative Banach algebras. Scientifical researcher at the Institute of Mathematics of the Romanian Academy, where some results in Banach algabras, Harmonic analysis, Operator theory and Prediction theory were obtained.
• Doctor in Mathematics since 1979.
• The main results was obtained in Operator Theory and in Prediction Theory. Using operator techniques and dilation theory, results from q-variate prediction to infinite-variate case was extended. A consistent theory of operatorial prediction was done in the discrete and continuous unitime and some results in multitime prediction were obtained. Also, some connections between the operatorial maximal function of a contraction and linear systems having the main operator a contraction was given
• Simion Stoilow Prize of the Romanian Academy (1979), for results in Prediction Theory.
• Member of the Romanian Mathematical Society.
• Member of the American Mathematical Society.
• Reviewer to Zentralblatt fur Math., Reviewer to Math Reviews, etc.
• Teaching on Functional analysis, Operator theory and Operatorial models in prediction to the University of Bucharest, University of Timisoara, and Polytechnical University Bucharest.
• Participation to various international Conferences on Mathematics. (e.g., OT-Conferences Timisoara, ICM-78 Helsinki, Romanian-Finnish Seminar on Complex Analysis, Banach Center-Warsaw, Poland, Various Conferences in Czechoslovakia, Bulgaria, Ukraina, Germany, Sweden, Italy, Finland, MTNS-93 Regensburg, IWOTA-95 Regensburg, ICIAM-95 Hamburg, IWOTA-96 Bloomington, MTNS-96 St. Louis, USA, WONRA-96 Sapporo, Japan, ICIAM-99 Edinborough, MTNS-2000 Perpignan, France, ICTAMI-2007, European Congres of Math. (5ECM) Amsterdam 2008, ICTAMI-2009, 2011, AMS Conference Alba Iulia 2012, IWOTA-2014 Amsterdam,OT-2014, The eight Congress of Romanian Mathematicians. Iasi-2015, IWOTA-2015 Tbilisi, Georgia, OT-2016, The 7-th European Congress of Math., 7ECM-2016, Berlin, WONRA Conference Lisabona, Portugal, 2016 and other Worksops in Functional Analysis and Operator Theory).

List of publications:

I. Articles:

1. Discuri analitice în algebre Banach comutative, Dissertation, Universitatea din Timisoara, 1970
2. Dilatarea unitara simultana a unui sistem comutativ de contractii si inegalitatea von Neumann, Preprint (1973). (colab. I.Suciu)
3. On the hyperbolic metric on Harnack parts, Studia Mathematica, Tom 55 (1976), 97-109. (colab. I. Suciu)
4. Factorization of semispectral measures, Rev. Roum. Math. Pures et Appl. Tome XXI Nr. 6 (1976), 773-793. (colab. I. Suciu)
5. On the hyperbolic metric on Harnack parts II, Studia Mathematica 58 (1976), 99-100. (colab. I. Suciu)
6. Essential parameters in prediction, Rev. Roum. Math. Pures et Appl. Rom XXXII, Nr. 10 (1977), 1477-1495. (colab. I. Suciu)
7. Factorization theorems and prediction theory, Rev. Roum. Math. Pures et Appl. Tom XXIII, Nr. 9 (1978), 1393-1423. (colab. I. Suciu)
8. Fatou and Szego theorems for operator valued functions, Proc. of Romanian-Finnish Seminar on Complex Analysis 1976, Lecture Notes in Math. 743 (1979), 656-673. (colab. I. Suciu)
9. On the maximal outer function of a semispectral measure, Proc. Coll.on Complex Analysis, Joensuu, Finland 1978. Springer Verlag vol. 747 (1979), 409-416
10. On the Harnack parts of completely positive maps, SLOHA Nr.3, Timisoara (1979) 1-28. (colab. I. Suciu)
11. Wold decomposition theorem for continuous parameter stationary processes in complete correlated actions, Proc. of the fourth Conf. on Operator Theory (1979), 88-104.
12. A linear filtering problem in complete correlated actions, Journal of Multi variate Analysis, Vol. 9, Nr. 4 (1979), 599-613. (colab. I. Suciu)
13. The maximal function of a contraction, Acta Scientiarum Math., Vol. 42 (1980), 183-188.
14. Metode operatoriale in teoria predictiei I., St. Cerc. Mat. Tom 33, Nr. 3 (1981), 343-401.
15. Metode operatoriale in teoria predictiei II., St. Cerc. Mat. Tom 33, Nr. 4 (1981), 467-492.
16. Linear predictor for stationary processes in complete correlated actions, Spectral Theory, Banach Center Publ. Vol. 8 (1981), 435-447. (colab. I. Suciu)
17. The maximal function of doubly commuting contradictions, Operator Theory, Adv. and Appl. Vol. 2 (1982), 295-309, Birkhauser. (colab. N. Suciu)
18. On stationary processes in complete correlated actions, Lecture Notes in Math. 1014 (1983), 316-334.
19. Continuous stationary processes in complete correlated actions, Prediction Theory and Harmonic Analysis, Pesi Masani Volume, North Hololand Pub. Co. (1983), 431-446.
20. Procese armonizabile în actiuni corelate complete, Contract INCREST (1984), 12 pag.
21. On the extension theorem for completely positive maps, Proc. Of Coll. On Banach Algebras, Poland (1985). (colab. I. Suciu)
22. On a certain class of operator valued analytic functions on the bidisc, SLOHA Nr.5 (1986), 16p. (Zbl 0686.47020).
23. Functii de tip Wold si structuri analitice asociate representarilor izometrice 2-generate, An. Univ. Timisoara (1986) (colab. D. Gaspar and N. Suciu)
24. Semispectral measures on the bitorus and Wold-type functions on the bidisc, Sem.Oper.Liniari Anal. Armonica (SLOHA) nr.3 (1987), 22p (Zbl 0825.47004). (Colab. D. Gaspar and N. Suciu)
25. Factorization and the Szego theorem for semispectral measures on $\mathbb{T}^2$. The 12-th Conf. on Operator Theory, 1988, 37-42.
26. Semispectral measures, Wold-type functions and stationary processes on $\mathbb{T}^2$. Preprint, INCREST (1989).
27. On a certain class of operator valued analitic functions on the bidisc, An. Univ. Timisoara, Nr. 27 (1989), 41-48. (colab. D. Gaspar and N. Suciu)
28. Operator valued function on bidisc and prediction, MTNS - 1991. (colab. D. Gaspar and N. Suciu)
29. Operatorial models for stationary processes, Special Topics in Modern Analysis, Mon. Math. Nr. 47 (1991), 57-84. (Colab. I. Suciu)
30. Semispectral measures on the bitorus and Wold-type functions on the bidisc, Rev. Roumaine Math. Pures et Appl. Tome 38 Nr. 3(1993), 253-266. (colab. D. Gaspar and N. Suciu)
31. Discrete two-time parameter stationary processes, On occ. 80th aniv. Prof. B.Sz.-Nagy, Szeged 1993. (colab. D. Gaspar si N. Suciu)
32. On some operator-valued functions on bidisc and prediction theory, Proc. MTNS-93,(Helmke Uwe & all eds.) Math. Research Vol. 79 (1994), 685-686. (colab. D. Gaspar and N. Suciu)
33. On some Operatorial Non-stationary Harmonizable Processes, Preprint, Grant Romanian Academy/1996.
34. Operatorial Non-Stationary Harmonizable Processes, Z. Angew. Math. Mec. 76 (1996), 695-696.
35. On quarter plane prediction, IWOTA-96, Bloomington, Indiana University, 1996.
36. An operatorial view on infinite-variate prediction, MTNS-1996, St. Louis, 1996.
37. On the maximal function and applications, WONRA-96 Conf. Sapporo, Japan, 1996.
38. On the maximal function of a semispectral measure, Workshop Funct.Analysis and Appl. Nemecka 1997, p. 40-41. (colab. I. Suciu)
39. Some applications of the maximal function, Krein Conf. Odessa 1997. (colab. I. Suciu)
40. Spectral analysis and prediction of two-time parameter stationary processes, Special Topics on Operator Theory, Timisoara 6-10 Oct. 1997. (colab D. Gaspar and N. Suciu)
41. On discrete time infinite-variate prediction, Proc. MTNS-98, Padova 1998. p.883-887.(colab. I. Suciu)
42. $\mathbb{Z}^2$-indexed operator systems and semispectral measures, Grant MCT-4073/1998, 8p. (colab. I. Suciu)
43. Dilations and factorization of semispectral measures, Preprint Grant MCT 1998. (colab. I. Suciu)
44. Models for discrete time infinite-variate prediction, Preprint Grant Romanian Academy/1998. (colab. I. Suciu)
45. Factorization of operatorial valued functions and applications, National Conf. on Math. Analysis and Appl., Timisoara 14-15 Nov. 1998
46. On the maximal function of a semispectral measure, ICIAM-99, Edinborough, 1999.
47. On periodic correlated processes, Proc. Conf. Functional Analysis and Appl.,Nemecka, Slovakia, 1999, p.72-74.
48. On a nonstationary process with periodic correlations, Com. Conf. B.Sz.-Nagy, Szeged, 1999.
49. An operatorial view on periodic correlated processes, CD of MTNS-2000, Perpignan, France,2000.
50. On periodically processes in complete correlated actions, The 6-th Cong. Roum. Math., Bucuresti, 2007.
51. On nonstationary periodically correlated processes in complete correlated actions, Acta Univ. Apulensis, Nr.15 (2008), p. 353-372.
52. A linear filter for the operatorial prediction of a periodically correlated process, Rev. Roumaine Math. Pures et Appl., Tome 54 nr. 1 (2009), 53-67.
53. Some remarks on periodically correlated processes in complete correlated actions, Inst. Math. "Simion Stoilow", Preprint IMAR Nr. 5/2008.
54. On periodic estimation in complete correlated actions, The 11-th Romanian-Finnish Seminar, Alba Iulia, 2008.
55. Simultaneous dilation of a commutative system of contractions and von Neumann inequality, An. Univ.Timisoara, Ser. Math-Inf., Vol. 47, ( 2009), 133-150.
56. Spectral factors and the maximal function , An. Univ. Timisoara, Vol. 47, (2009), 151-163.
57. Some remarks on the maximal function , Proc. ICTAMI-2009 (D. Breaz, N. Breaz and D. Weinberg eds.) Acta Univ. Ap., Special Issue (2009), 195-2007.
58. Some connections between the maximal function and systems , Math. Reports Vol. 12(2010), 189-199.
59. An update on the maximal function , Preprint IMAR nr.8/2009.
60. Notes on continuous parameter periodically $\Gamma$-correlated processes , An. Univ. Timisoara, Vol 50 (2012), 115-125.
61. A new update on the maximal function , OT-23, Timisoara, 2010.
62. On uniformly bounded linearly $\Gamma$-stationary processes, ICNAAM-2010, Rodos, (T.Simos and G.Psihoyios eds.), AIP Conf. Proceedings, Vol. 1281(2010), 432-435.
63. $\Gamma$-correlated processes. Some geometrical considerations. Preprint IMAR Nr. 7/2011, 12 pag.
64. Connections between the maximal function and systems. International Workshop on Functional Analysis WFA-2012, Timisoara, 12-14 oct. 2012.
65. On the functional model of the maximal function of a contraction operator, IWOTA-2014, Amsterdam, 14-18 July 2014.
66. Some geometrical aspects of the $\Gamma$-correlated processes, An. Univ. Oradea, Tom XXI (2014),113-123.
67. On the Friedrichs angle between past and future, Proc. ICTAMI-2011, Acta Univ Ap., Special Issue (2011), 85-94
68. Some remarks on the infinite variate prediction I. Proc. int. conf. Classical and Functional Analysis, Azuga, 2013. Transilvania University Press, Brasov, 2014, pag.74-102.
69. Some remarks on the infinite variate prediction II. Proc. int. conf. Classical and Functional Analysis, Busteni, 2014. Transilvania University Press, Brasov (to appear 2015)
70. The maximal function of n-hypercontractions, (in preparation).

II. Books:

• Stationary processes in complete correlated actions , Mon. Math. Vol. 80, Universitatea de Vest, Timisoara, 2007. ISSN 1453-7702.
• Stochastic processes in correlated actions , Mon. Math., Vol. 83, Universitatea de Vest, Timisoara, 2008. ISSN 1453-7702.
• Book Chapter: On stationary processes in complete correlated actions, Lecture Notes in Math. Vol. 1014(1983), ISBN 0-387-12683-X. DOI: 10.1007/BFb0072090. (http://www.springerlink.com/)
• Operatorial Prediction Theory (in preparation).

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