Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 14.10.1952
E-mail:
Keywords: multiple trigonometric Fourier series, Walsh–Fourier series, Fourier integrals, generalized localization, weak generalized localization, convergence, divergence, Weyl multipliers, structure and geometry characteristics of sets of convergence and divergence, lacunary sequences.
UDC: 517.5, 517.51

Subject:

Real Analysis, multidimensional Harmonic Analysis, problems of convergence of multiple Fourier expansions

Main publications:

1. I. L. Bloshanskii, “Uniform convergence of expansions into a multiple trigonometric Fourier series or a Fourier integral”, Math. Notes, 18:2 (1975), 675–684        
2. I. L. Bloshanskii, “Equiconvergence of expansions in a multiple Fourier series and Fourier integral for summation over squares”, Math. USSR-Izv., 10:3 (1976), 652–671        
3. I. L. Bloshanskii, “On the convergence of double Fourier series of functions from $L_p$, $p>1$”, Math. Notes, 21:6 (1977), 438–444        
4. I. L. Bloshanskii, “Generalized localization almost everywhere and convergence of double Fourier series”, Sov. Math. Dokl., 19 (1978), 1019-1023        
5. I. L. Bloshanskii, “Generalized localization and convergence tests for double trigonometric Fourier series of functions from $L_p$, $p > 1$”, Analysis Mathematica, 7:1 (1981), 3-36        
6. I. L. Bloshanskii, “Generalized lokalization for multiple Fourier series and the geometry of measurable sets in N-dimensional space”, Soviet Math. Dokl., 26 (1982), 405–409        
7. I. L. Bloshanskii, “On the geometry of measurable sets in $N$-dimensional space on which generalized localization holds for multiple trigonometric Fourier series of functions from $L_p$, $p>1$”, Math. USSR-Sb., 49:1 (1984), 87–109        
8. I. L. Bloshanskii, “On criteria for weak generalized localization in $N$-dimensional space”, Sov. Math. Dokl., 28 (1983), 244-248      
9. I. L. Bloshanskii, “Two criteria for weak generalized localization for multiple trigonometric Fourier series of functions in $L_p$, $p\geqslant1$”, Math. USSR-Izv., 26:2 (1986), 223–262        
10. I. L. Bloshanskii, “On the divergence of a Fourier series almost everywhere on a given set, and convergence to zero outside it”, Sov. Math., Dokl., 31 (1985), 139-142        
11. 15. I. L. Bloshanskii, “On maximal sets of convergence and unbounded divergence of multiple Fourier series of functions in $L_1$ that are equal to zero on a given set”, Sov. Math., Dokl, 32 (1985), 232-235      
12. 16. I. L. Bloshanskii, “On some questions of square convergence of multiple Fourier series and integrals of functions in $L_1$”, Sov. Math., Dokl., 35:3 (1987), 475-478        
13. I. L. Bloshanskii, “On the existence of functions from $L_p$, $p \ge 1$., whose Fourier series converge to zero on a prescribed set and diverge unboundedly outside it.”, Analysis Mathematica, 14:1 (1988), 139-155        
14. I. L. Bloshanskii, “The structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere of multiple Fourier series of functions in $L_1$ equal to zero on a given set”, Math. USSR-Izv., 35:1 (1990), 1–35        
15. I. L. Bloshanskii, “Multiple Fourier integral and multiple Fourier series under square summation”, Sib. Math. J., 31:1 (1990), 30–42            
16. I. L. Bloshanskii, “Weyl multipliers and the growth of the partial sums of rectangularly summable multiple trigonometric Fourier series”, Soviet Math. Dokl., 44:3 (1992), 749–752      
17. 16. I. L. Bloshanskii, “Correlation between the structure and geometry of sets of unbounded divergence and a method of summing a multiple Fourier series of a function in $L_p$, $p>1$, that is equal to zero on a certain set”, Sov. Math., Dokl., 44:3 (1992), 843-847      
18. I. L. Bloshanskii, “On sequences of linear operators”, Proc. Steklov Inst. Math., 201 (1994), 35–63      
19. I. L. Bloshanskii, “The exact Weyl multiplier for the validity of generalized localization on any open sets for rectangularly summed tree-dimensional Fourier series”, Soviet Math. Dokl., 45:1 (1992), 215–220      
20. I. L. Bloshanskii, S. K. Bloshanskaya, “Generalized and weak generalized localization for multiple Fourier-Walsh functions in $L_p, p\ge1$”, Soviet Math. Dokl., 48:2 (1994), 359–364          
21. S. K. Bloshanskaya, I. L. Bloshanskii, “Generalized localization for the multiple Walsh–Fourier series of functions in $L_p$, $p\geqslant 1$”, Sb. Math., 186:2 (1995), 181–196          
22. I. L. Bloshanskii, O. K. Ivanova, T. Yu. Roslova, “Generalized localization and equiconvergence of expansions in double trigonometric series and in the Fourier integral for functions from $L(\ln^+L)^2$”, Math. Notes, 60:3 (1996), 324–327              
23. , I. L. Bloshanskii, S. K. Bloshanskaya, “Weak generalized localization for multiple Fourier–Walsh series of functions in $L_p$, $p\ge 1$”, Proc. Steklov Inst. Math., 214 (1996), 77–100      
24. I. L. Bloshanskii, S. K. Bloshanskaya, T. Yu. Roslova, “Generalized localization for the double trigonometric Fourier series and the Walsh–Fourier series of functions in $L\log^+L\log^+\log^+L$”, Sb. Math., 189:5 (1998), 657–682              
25. I. L. Bloshanskii, T. A. Matseevich, “Slabaya obobschennaya lokalizatsiya dlya kratnykh ryadov Fure nepreryvnykh funktsii s nekotorym modulem nepreryvnosti”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza. Sbornik statei, Izdatelstvo AFTs, g. Moskva, 1999, 37 – 56 (ISBN 5-93379-002-8).  
26. I. L. Bloshanskii, “O mnozhestvakh neogranichennoi raskhodimosti v kazhdoi tochke kratnogo ryada Fure funktsii, ravnoi nulyu na zamknutom mnozhestve”, Analysis Mathematica, 26:2 (2000), 81 -98        
27. I. L. Bloshanskii, “A criterion for weak generalized localization in the class $L_1$ for multiple Fourier trigonometric series from the point of view of isometric transformations”, Math. Notes, 71:4 (2002), 464–476                
28. I. L. Bloshanskii, “Structural and Geometric Characteristics of Sets of Convergence and Divergence of Multiple Fourier Series of Functions which Equal Zero on Some Set”, International Journal of Wavelets, Multiresolution and Information Processing, 2:2, World Scientific Publishing Company. New Jersey - London- Singapore - Hong Kong (2004), 187 -195 (ISBN 981-238-342-5/hbk/set)      
29. I. L. Bloshanskii, “Linear transformations of $R^N$ and problems of convergence of multiple Fourier integral”, Wavelet Analysis and Active Media Technology. Proceedings of the 6-th International Progress, 3, World Scientific Publishing Company, New Jersey – London – Singapore – Hong Kong., 2005, 1061 –1091.
30. I. L. Bloshanskii, T. A. Matseevich, “A Weak Generalize Localization of Multiple Fourier Series of Continuous Functions with a Certain Module of Continuity”, Journal of Mathematical Sciences, 155:1 (2008), 31–46          
31. I. L. Bloshanskii, “Linear transformations of $R^N$ and problems of convergence of multiple Fourier Series of functions which equal zero on some set.”, Applied and Numerical Harmonic Analysis. Springer Book Series (SCI). Volume “Wavelet Analysis and Applications”., Selected papers based on the presentations at the conference (WAA 2005), Macau, China, 29th November – 2nd December 2005. With CD-ROM., (ISBN 3-7643-7777-1/hbk), Basel: Birkhäuser, 2007, 13 – 24.      
32. I. L. Bloshanskii, S. K. Bloshanskaya, “Local Smoothness Conditions on a Function which Guarantee Convergence of Double Walsh-Fourier Series of this Function”, Applied and Numerical Harmonic Analysis. Springer Book Series (SCI). Volume “Wavelet Analysis and Applications”, Basel: Birkhaüser, 2007, 3 – 11 (ISBN 3-7643-7777-1/hbk)    
33. I. L. Bloshanskii, T .A. Matseevich, “A weak generalized localization of multiple Fourier series of continuous functions with a certain module of continuity.”, J. Math. Sci., New York, 155:1 (2008), 31–46          
34. I. L. Bloshanskii, “Strukturnye i geometricheskie kharakteristiki mnozhestv skhodimosti i raskhodimosti kratnykh razlozhenii Fure funktsii, ravnykh nulyu na nekotorom mnozhestve”, Vestnik MGOU, 2007, 3-13 (to appear)      
35. I. L. Bloshanskii, O. V. Lifantseva, “Weak Generalized Localization for Multiple Fourier Series Whose Rectangular Partial Sums Are Considered with Respect to Some Subsequence”, Math. Notes, 84:3 (2008), 314–327                  
36. I. L. Bloshanskii, O. V. Lifantseva, “A weak generalized localization criterion for multiple Fourier series whose rectangular partial sums are considered over a subsequence”, Dokl. Math., 78:3 (2008), 864-867          
37. I. L. Bloshanskii, Information computing and automation. Proceedings of the international conference, China, December 20–22, 2007. 3 Vols. (English), eds. Li, Jian Ping; Bloshanskii, Igor ; Ni, Lionel M.; Pandey, S. S.; Yang, Simon X., Hackensack, NJ: World Scientific, 2008, 1554 pp.  
38. I. L. Bloshanskii, O. V. Lifantseva, “Maximal Sets of Convergence and Unbounded Divergence of Multiple Fourier Series with $J_k$-Lacunary Sequence of Partial Sums”, Math. Notes, 86:6 (2009), 883–886                  
39. I. L. Bloshanskii, “Linear Transformations of $R^N$ and Problems of Convergence of Multiple Fourier Series of Functions in $L_p, p > 1$”, Acta Sci. Math., 75:34 (2009), 575 –603, ISBN 0016969. (Szeged (Hungary))      
40. I. L. Bloshanskii, O. V. Lifantseva, “On $J_k$-lacunary sequences of rectangular partial sums of multiple Fourier series”, Progress in analysis. Proceedings of the 8th congress of the International Society for Analysis, its Applications, and Computation (ISAAC) (Russia, August 22–27, 2011.), 2, Moscow: Peoples’ Friendship University of Russia, 2012, 257-264 (ISBN 978-5-209-04590-8/hbk)  
41. I. L. Bloshanskii, S. K. Bloshanskaya, O. V. Lifantseva, “Trigonometric Fourier Series and Walsh–Fourier Series with Lacunary Sequence of Partial Sums”, Math. Notes, 93:2 (2013), 332–336                  
42. I. L. Bloshanskii, D. A. Grafov, “Equiconvergence of Expansions in Multiple Trigonometric Fourier Series and Integrals in the Case of a Lacunary Sequence of Partial Sums”, Doklady Mathematics, 87:3 (2013), 1–4          
43. I. L. Bloshanskii, O. V. Lifantseva, “Structural and Geometric Characteristics of Sets of Convergence and Divergence of Multiple Fourier Series with Jk -lacunary Sequence of Rectangular Partial Sums”, Analysis Mathematica, 39:2 (2013), 93 - 121, (ISSN: 0133-3852).          
44. I. L. Bloshanskii, S K. Bloshanskaya, O. V. Lifantseva, “Multiple Fourier Expansions over Walsh-Paley and Trigonometric Systems”, ‘Kangro-100. Methods of Analysis and Algebra International Conference dedicated to the Centennial of Professor Gunnar Kangro’' (Tartu, Estonia, September 1-6, 2013), Institute of Mathematics, University of Tartu, Estonian Mathematical Society. Tartu, 2013, 85-86 (ISBN: 978-9949-9180-6-5).
45. I. L. Bloshanskii, D. A. Grafov, ““Almost” Cauchy Property for the Sequence of Partial Sums of Fourier Series of Functions in $L_p$, $p > 1$”, ‘Kangro-100. Methods of Analysis and Algebra International Conference dedicated to the Centennial of Professor Gunnar Kangro’' (Tartu, Estonia, September 1-6, 2013), Institute of Mathematics, University of Tartu, Estonian Mathematical Society., Tartu, 2013, 63-64. (ISBN: 978-9949-9180-6-5).
46. I. L. Bloshanskii, O. V. Lifantseva, “Structural and Geometric Characteristics of Sets of Convergence and Divergence of Multiple Fourier Series with $J_k$ -lacunary Sequence of Rectangular Partial Sums”, Analysis Mathematica, 39:2 (2013), 93 - 121 (ISSN: 0133-3852)        
47. I. L. Bloshanskii, Z. N. Tsukareva, “Localization for Multiple Fourier Series with "$J_k$-Lacunary Sequence of Partial Sums" in Orlicz Classes”, Math. Notes, 95:1 (2014), 22–31                
48. I. L. Bloshanskii, S. K. Bloshanskaya, “A weak generalized localization criterion for multiple Walsh–Fourier series with $J_k$-lacunary sequence of rectangular partial sums”, Proc. Steklov Inst. Math., 285 (2014), 34–55              
49. I. L. Bloshanskii, D. A. Grafov, “Ravnoskhodimost razlozhenii v kratnyi ryad i integral Fure, “pryamougolnye chastichnye summy” kotorykh rassmatrivayutsya po nekotoroi podposledovatelnosti”, Analysis Mathematica, 40:3 (2014), 175-196, (ISSN: 0133-3852).        
50. I. L. Bloshanskii, D. A. Grafov, “Equiconvergence of expansions in multiple trigonometric Fourier series and Fourier integral with " $J_k$ - lacunary sequences of rectangular partial sums"”, Acta Et Commentationes Universitatatis Tartuensis de Mathematica, 18:1 (2014), 69–79, (ISSN: 1406-2283), http://acutm.math.ut.ee/index.php/acutm/article/view/ACUTM.2014.18.08/24      
51. I. L. Bloshanskii, D. A. Grafov, “Sufficient conditions for convergence almost everywhere of multiple trigonometric Fourier series with lacunary sequence of partial sums”, Real Analysis Exchange, Vol. 41(1) (2015/2016), 159–172, (ISSN: 0147-1937).        
52. I. L. Bloshanskii, D. A. Grafov, “Equiconvergence of Expansions in Multiple Fourier Series and in Fourier Integrals with “Lacunary Sequences of Partial Sums””, Math. Notes, 99:2 (2016), 196–209                
53. I. L. Bloshanskii, S. K. Bloshanskaya, “Convergence and localization in Orlicz classes for multiple Walsh-Fourier series with a lacunary sequence of rectangular partial sums”, J. Math. Anal. Appl., 435 (2016), 765–782, ISSN: 0022-247X (http://dx.doi.org/10.1016/j.jmaa.2015.10.018)            
54. I .L. Bloshanskii, S. K. Bloshanskaya, D. A. Grafov, Sufficient conditions for convergence of multiple Fourier series with Jk-lacunary sequence of rectangular partial sums in terms of Weyl multipliers, 2017 (Published online), 29 pp., arXiv: 1704.04673 [math.CA].    
55. I. L. Bloshanskii, S. K. Bloshanskaya, D. A. Grafov, “Sufficient conditions for convergence of multiple Fourier series with Jk-lacunary sequence of rectangular partial sums in terms of Weyl multiplier”, Acta Sci. Math., 83:3-4 (2017), 511–537, ISSN: 0001-6969, (Szeged (Hungary)          

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Organisations:

• Moscow State Region University
• Lomonosov Moscow State University
• Moscow State Pedagogical University
• Moscow Mathematical Society