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Shevaldin, Valerii Trifonovich
Statistics Math-Net.Ru
Total publications: 55
Scientific articles: 53

Number of views:
This page:5591
Abstract pages:15322
Full texts:5404
References:1755
Senior Researcher
Doctor of physico-mathematical sciences (1996)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 18.08.1955
E-mail:
Keywords: extremal interpolation in the mean, splines
UDC: 517.5, 517.9, 519.65, 517, 518.12, 517.518.8, 5175

Subject:

Theory of approximation of functions
   
Main publications:
  1. V.T. Shevaldin, “Ob odnoi zadache ekstremalnoi interpolyatsii”, Matematicheskie zametki, 29:4 (1981), 603-622
  2. V.T. Shevaldin, “Ekstremalnaya interpolyatsiya s naimenshim znacheniem normy lineinogo differentsialnogo operatora”, Matematicheskie zametki, 27:5 (1980), 721-740
  3. V.T. Shevaldin, “Ekstremalnaya interpolyatsiya v srednem pri perekryvayuschikhsya intervalakh usredneniya s naimenshim znacheniem normy lineinogo differentsialnogo operatora”, Trudy Instituta matematiki i mekhaniki UrO RAN, 29:1 (2023), 219-232
  4. V.T. Shevaldin, “Nekotorye zadachi ekstremalnoi interpolyatsii v srednem dlya lineinykh differentsialnykh operatorov”, Trudy MIAN SSSR, 164 (1983), 203-240
  5. V.T. Shevaldin, “Ekstremalnaya interpolyatsiya v srednem pri perekryvayuschikhsya intervalakh usredneniya i L-splainy”, Izvestiya RAN. Seriya matematicheskaya, 62:4 (1998), 201-224

https://www.mathnet.ru/eng/person8871
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/206798

Publications in Math-Net.Ru Citations
2024
1. S. E. Nohrin, V. T. Shevaldin, “Sufficient conditions for the existence of the solution of an infinite-difference equation with variable coefficients”, Chebyshevskii Sb., 25:2 (2024),  243–250  mathnet
2. V. T. Shevaldin, “Yu. N. Subbotin's Method in the Problem of Extremal Interpolation in the Mean in the Space $L_p(\mathbb R)$ with Overlapping Averaging Intervals”, Mat. Zametki, 115:6 (2024),  919–934  mathnet  mathscinet; Math. Notes, 115:6 (2024), 1017–1029  scopus
3. V. T. Shevaldin, “Extremal Interpolation in the Mean in the Space $L_1(\mathbb R)$ with Overlapping Averaging Intervals”, Mat. Zametki, 115:1 (2024),  123–136  mathnet  mathscinet; Math. Notes, 115:1 (2024), 102–113  scopus 1
2023
4. V. T. Shevaldin, “Local Extremal Interpolation on the Semiaxis with the Least Value of the Norm for a Linear Differential Operator”, Mat. Zametki, 113:3 (2023),  453–460  mathnet  mathscinet; Math. Notes, 113:3 (2023), 446–452  scopus
5. V. T. Shevaldin, “Extremal interpolation in the mean with overlapping averaging intervals and the smallest norm of a linear differential operator”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:1 (2023),  219–232  mathnet  mathscinet  elib 2
6. V. T. Shevaldin, “On Favard local parabolic interpolating splines with additional knots”, Zh. Vychisl. Mat. Mat. Fiz., 63:6 (2023),  979–986  mathnet  elib; Comput. Math. Math. Phys., 63:6 (2023), 1045–1051
2022
7. V. T. Shevaldin, “Extremal interpolation with the least value of the norm of the second derivative in $L_p(\mathbb R)$”, Izv. RAN. Ser. Mat., 86:1 (2022),  219–236  mathnet  mathscinet; Izv. Math., 86:1 (2022), 203–219  isi  scopus 1
8. Yu. N. Subbotin, V. T. Shevaldin, “Extremal functional $L_p$-interpolation on an arbitrary mesh on the real axis”, Mat. Sb., 213:4 (2022),  123–144  mathnet  mathscinet; Sb. Math., 213:4 (2022), 556–577  isi  scopus 2
9. V. T. Shevaldin, “On Yu. N. Subbotin's Circle of Ideas in the Problem of Local Extremal Interpolation on the Semiaxis”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:4 (2022),  237–249  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S229–S241  isi  scopus
2021
10. V. T. Shevaldin, “Subbotin's splines in the problem of extremal interpolation in the space $L_p$ for second-order linear differential operators”, Trudy Inst. Mat. i Mekh. UrO RAN, 27:4 (2021),  255–262  mathnet  elib
2020
11. V. T. Shevaldin, “Local approximation by parabolic splines in the mean with large averaging intervals”, Mat. Zametki, 108:5 (2020),  771–781  mathnet  mathscinet  elib; Math. Notes, 108:5 (2020), 733–742  isi  scopus
12. S. I. Novikov, V. T. Shevaldin, “Extremal interpolation on the semiaxis with the smallest norm of the third derivative”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:4 (2020),  210–223  mathnet  elib 1
13. S. I. Novikov, V. T. Shevaldin, “On the connection between the second divided difference and the second derivative”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:2 (2020),  216–224  mathnet  elib 7
2019
14. V. T. Shevaldin, “Algorithms for the construction of third-order local exponential splines with equidistant knots”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:3 (2019),  279–287  mathnet  elib 1
15. Yu. N. Subbotin, V. T. Shevaldin, “A Method for the Construction of Local Parabolic Splines with Additional Knots”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:2 (2019),  205–219  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S151–S166  isi  scopus 2
2018
16. Yu. N. Subbotin, S. I. Novikov, V. T. Shevaldin, “Extremal functional interpolation and splines”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:3 (2018),  200–225  mathnet  elib 13
17. V. T. Shevaldin, “On integral Lebesgue constants of local splines with uniform knots”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:2 (2018),  290–297  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S158–S165  isi  scopus 2
2017
18. V. T. Shevaldin, O. Ya. Shevaldina, “The Lebesgue constant of local cubic splines with equally-spaced knots”, Sib. Zh. Vychisl. Mat., 20:4 (2017),  445–451  mathnet  elib; Num. Anal. Appl., 10:4 (2017), 362–367  isi  scopus 3
19. V. T. Shevaldin, “Uniform Lebesgue constants of local spline approximation”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:3 (2017),  292–299  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 196–202  isi
20. Valerii T. Shevaldin, “Calibration relations for analogues of the basis splines with uniform nodes”, Ural Math. J., 3:1 (2017),  76–80  mathnet  mathscinet  elib
2016
21. V. T. Shevaldin, “A method for the construction of analogs of wavelets by means of trigonometric $B$-splines”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:4 (2016),  320–327  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 165–171  isi  scopus
22. E. V. Strelkova, V. T. Shevaldin, “On uniform Lebesgue constants of third-order local trigonometric splines”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:2 (2016),  245–254  mathnet  mathscinet  elib 1
2015
23. V. T. Shevaldin, O. Ya. Shevaldina, “Upper bounds for uniform Lebesgue constants of interpolational periodic sourcewise representable splines”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:4 (2015),  309–315  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 175–181  isi 1
24. E. V. Strelkova, V. T. Shevaldin, “On uniform Lebesgue constants of local exponential splines with equidistant knots”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:4 (2015),  261–272  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 206–217  isi 5
25. E. G. Pytkeev, V. T. Shevaldin, “Two-scale relations for $B$-$\mathcal L$-splines with uniform knots”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:4 (2015),  234–243  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 186–195  isi 1
26. E. V. Strelkova, V. T. Shevaldin, “On Lebesgue constants of local parabolic splines”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:1 (2015),  213–219  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 192–198  isi  scopus 4
2014
27. E. V. Strelkova, V. T. Shevaldin, “Local exponential splines with arbitrary knots”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:1 (2014),  258–263  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 189–194  isi  scopus 2
2012
28. Yu. S. Volkov, V. T. Shevaldin, “Shape preserving conditions for quadratic spline interpolation in the sense of Subbotin and Marsden”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:4 (2012),  145–152  mathnet  elib 10
29. Yu. S. Volkov, E. G. Pytkeev, V. T. Shevaldin, “Orders of approximation by local exponential splines”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:4 (2012),  135–144  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 175–184  isi  scopus 2
2011
30. Yu. S. Volkov, E. V. Strelkova, V. T. Shevaldin, “Local approximation by splines with displacement of nodes”, Mat. Tr., 14:2 (2011),  73–82  mathnet  mathscinet  elib; Siberian Adv. Math., 23:1 (2013), 69–75 7
31. V. T. Shevaldin, “Two-scale relations for analogs of basis splines of small degrees”, Trudy Inst. Mat. i Mekh. UrO RAN, 17:3 (2011),  319–323  mathnet  elib 1
32. E. V. Strelkova, V. T. Shevaldin, “Form preservation under approximation by local exponential splines of an arbitrary order”, Trudy Inst. Mat. i Mekh. UrO RAN, 17:3 (2011),  291–299  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 171–179  isi  scopus 3
2010
33. Yu. S. Volkov, V. V. Bogdanov, V. L. Miroshnichenko, V. T. Shevaldin, “Shape-Preserving Interpolation by Cubic Splines”, Mat. Zametki, 88:6 (2010),  836–844  mathnet  mathscinet; Math. Notes, 88:6 (2010), 798–805  isi  scopus 20
34. E. V. Strelkova, V. T. Shevaldin, “Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a differential operator”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:4 (2010),  272–280  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S133–S141  isi  scopus 5
35. P. G. Zhdanov, V. T. Shevaldin, “Approximation by third-order local $\mathcal L$-splines with uniform nodes”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:4 (2010),  156–165  mathnet  elib
2006
36. V. T. Shevaldin, “Approximation by local $L$-splines corresponding to a linear differential operator of the second order”, Trudy Inst. Mat. i Mekh. UrO RAN, 12:2 (2006),  195–213  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 255, suppl. 2 (2006), S178–S197  scopus 6
2005
37. K. V. Kostousov, V. T. Shevaldin, “Approximation by local trigonometric splines”, Mat. Zametki, 77:3 (2005),  354–363  mathnet  mathscinet  zmath  elib; Math. Notes, 77:3 (2005), 326–334  isi  scopus 10
38. V. T. Shevaldin, “Approximation by local parabolic splines with arbitrary knots”, Sib. Zh. Vychisl. Mat., 8:1 (2005),  77–88  mathnet  zmath 16
2001
39. V. T. Shevaldin, “The Jackson–Stechkin inequality in the space $C(\mathbb T)$ with trigonometric continuity modulus annihilating the first harmonics”, Trudy Inst. Mat. i Mekh. UrO RAN, 7:1 (2001),  231–237  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2001no. , suppl. 1, S206–S213 1
40. S. I. Novikov, V. T. Shevaldin, “A problem of extremal interpolation for multivariate functions”, Trudy Inst. Mat. i Mekh. UrO RAN, 7:1 (2001),  144–159  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2001no. , suppl. 1, S150–S166 6
1999
41. A. G. Babenko, N. I. Chernykh, V. T. Shevaldin, “The Jackson–Stechkin inequality in $L^2$ with a trigonometric modulus of continuity”, Mat. Zametki, 65:6 (1999),  928–932  mathnet  mathscinet  zmath; Math. Notes, 65:6 (1999), 777–781  isi 11
1998
42. V. T. Shevaldin, “Extremal interpolation in the mean with overlapping averaging intervals and $L$-splines”, Izv. RAN. Ser. Mat., 62:4 (1998),  201–224  mathnet  mathscinet  zmath; Izv. Math., 62:4 (1998), 833–856  isi  scopus 7
1994
43. V. T. Shevaldin, “Lower estimates of the widths of the classes of functions defined by a modulus of continuity”, Izv. RAN. Ser. Mat., 58:5 (1994),  172–188  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 45:2 (1995), 399–415  isi 3
1993
44. V. T. Shevaldin, “Interpolating periodic splines and widths of classes of functions with a bounded noninteger derivative”, Dokl. Akad. Nauk, 328:3 (1993),  296–298  mathnet  mathscinet  zmath; Dokl. Math., 47:1 (1993), 79–82
45. V. T. Shevaldin, “Lower bounds for the widths of classes of periodic functions with a bounded fractional derivative”, Mat. Zametki, 53:2 (1993),  145–151  mathnet  mathscinet  zmath; Math. Notes, 53:2 (1993), 218–222  isi 1
1992
46. V. T. Shevaldin, “Widths of classes of convolutions with Poisson kernel”, Mat. Zametki, 51:6 (1992),  126–136  mathnet  mathscinet  zmath; Math. Notes, 51:6 (1992), 611–617  isi 5
47. V. T. Shevaldin, “Lower estimations of widths some classes of periodic functions”, Trudy Mat. Inst. Steklov., 198 (1992),  242–267  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 198 (1994), 233–255 2
1989
48. V. T. Shevaldin, “Lower bounds on widths of classes of sourcewise representable functions”, Trudy Mat. Inst. Steklov., 189 (1989),  185–200  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 189 (1990), 217–234 5
1983
49. V. T. Shevaldin, “$\mathscr L$-Splines and widths”, Mat. Zametki, 33:5 (1983),  735–744  mathnet  mathscinet  zmath; Math. Notes, 33:5 (1983), 378–383  isi 7
50. V. T. Shevaldin, “Some problems of extremal interpolation in the mean for linear differential operators”, Trudy Mat. Inst. Steklov., 164 (1983),  203–240  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 164 (1985), 233–273 27
1982
51. V. T. Shevaldin, “Some problems of extremal interpolation in the mean”, Dokl. Akad. Nauk SSSR, 267:4 (1982),  803–805  mathnet  mathscinet  zmath 2
1981
52. V. T. Shevaldin, “A problem of extremal interpolation”, Mat. Zametki, 29:4 (1981),  603–622  mathnet  mathscinet  zmath; Math. Notes, 29:4 (1981), 310–320  isi 20
1980
53. V. T. Shevaldin, “Extremal interpolation with least norm of linear differential operator”, Mat. Zametki, 27:5 (1980),  721–740  mathnet  mathscinet  zmath; Math. Notes, 27:5 (1980), 344–354  isi 7
2022
54. R. R. Akopyan, N. Yu. Antonov, V. V. Arestov, A. G. Babenko, N. V. Baidakova, V. I. Berdyshev, V. V. Vasin, S. I. Novikov, N. L. Patsko, A. G. Chentsov, N. I. Chernykh, V. T. Shevaldin, “Yurii Nikolaevich Subbotin (A Tribute to His Memory)”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:4 (2022),  9–16  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S1–S6  isi
2007
55. V. V. Arestov, V. I. Berdyshev, O. V. Besov, N. N. Krasovskii, S. M. Nikol'skii, S. I. Novikov, Yu. S. Osipov, S. A. Telyakovskii, N. I. Chernykh, V. T. Shevaldin, “Yurii Nikolaevich Subbotin (on his 70th birthday)”, Uspekhi Mat. Nauk, 62:2(374) (2007),  187–190  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 62:2 (2007), 403–406  isi 3

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