List of
Principal Publications
Alexander Petukhov
1. Approximation of discontinuous functions
in the Hausdorff metric (Russian),
Mat. Zametki 37 (1985), No 1, 25 - 40
(Math. Rev. 86 m:42007).
2. On snakes and the approximation of
discontinuous functions in the Hausdorff metric
(Russian, English summary), Analysis
Mathematica 11 (1985), No 1, 55 - 73
(Math. Rev. 87: a:42006).
3. The behavior of least polynomial
Hausdorff deviations from 2\pi-periodic functions
(Russian), Vestnik Moskov. Univ.
Ser. 1 Mat. Mekh. 1985, No 3, 11 -- 15
(Math. Rev. 87 i:42009).
4. On estimates for derivatives of
trigonometric polynomials (Russian),
Mat. Zametki 41 (1987), No
4, 517 - 520 (Math. Rev. 88 h: 42001).
5. Approximation of functions by singular
integrals in the Hausdorff metric (Russian),
Mat. Sborn. 135(177) (1988), No 2, 235
- 252 (Math. Rev. 89 j: 41034).
6. On dependence of properties of
function discontinuity points set upon the rate
of polynomial Hausdorff
approximation (Russian), Mat. Sborn. 136(178) (1989),
No 7, 969 -- 988.
7. On dependence of properties of the
function graphs upon the rate of its various
approximations (Russian),
Izv. Akad. Nauk SSSR, 55 (1991), No 1, 159 - 183.
8. On the approximation of functions by
convolutions in the Hausdorff metric
(Russian), Dokl. Russian Akad. Nauk ,
327(1992), No 2, 187 - 190
9. On convergence of sequences of
convolution operators in the Hausdorff metric
(Russian), Algebra i Analiz, 5
(1993), No 5, 87 - 117.
10. The space of almost periodic functions with
the Hausdorff metric
(Russian),
Mat. Sborn., 185 (1994), No 3, 69 - 92.
11. On approximation of periodic distributions
in the Hausdorff metric
(Russian),
Dokl. Russian Akad. Nauk, 336 (1994), No
1, 25 - 28.
12. On polinomials of the best approximation in
the Hausdorff metric (Russian)
Zapiski semimarov POMI, 217 (1994), 130 -
143.
13. On convergence of Fourier series of
functions of the classes
Besov --- Lizorkin --- Triebel in
the Hausdorff metric (Russian),
Mat. Zametki, 56 (1994), No 1, 63 - 70.
14. On convergence of Fourier series in the
Hausdorff metric,
Real An. Exch., 20 (1994 - 1995), No 1,
59 - 60.
15. Periodic discrete wavelets (Russian),
Algebra i Analiz, 8 (1996), No 3, 151 -
183.
Compressed Post Script files RUS(93
Kb), ENGL
(80 Kb)
16. Periodic wavelets: Construction and
Algorthms. Program on Spline
Functions and
the Theory of Wavelets. Abstracts.
Centre de Recherches Matematiques. Montreal, 1996.
17. Periodic wavelets (Russian), Mat.
Sborn. 188 (1997), No 10, 69 - 94.
Compressed Post Script files RUS(96
Kb), ENGL
(84 Kb)
18. Multiresolution analysis and wavelet
decompositions of spaces of
periodic distributions
(Russian), Dokl. Russian Akad. Nauk 356
(1997), No 2, 303 - 306.
Compressed Post Script file RUS(46 Kb)
19. Recursive filter banks and image
compression, Proceedings of the 3rd
St. Petersburg
Workshop on Simulation, June 28 - July
3, 1998, 381 - 383.
20. On approximation of generalized functions
by convolutions in the
Hausdorff metric
(Russian), Izv. Russian Akad. Nauk. Ser. Matem. (1999) (to appear).
21. Biorthogonal wavelet bases with rational
masks and their applications, Zapiski seminarov POMI (to
appear)
Compressed Post Script files RUS(99
Kb), ENGL
(83 Kb)
22. Trigonometric rational wavelet bases, Proceedings
of the International Workshop "Self-Similar Systems",
Dubna, July 30 - August, 7, 1998
Compressed Post Script files ENGL (26
Kb)
23. Introduction to the Theory of wavelet bases. St.Petersburg Technical University, 1999, 132 pages.
Compressed Post Script files RUS (350 Kb)
24. Wavelet-based video coding using image warping and overlapped block motion compensation (joint with D.Marpe, G.Heising, and H.L.Cycon), IEEE Trans. on circuits and systems for video technology (to appear)
Compressed Post Script files ENGL (591 Kb)
25. Explicit construction of framelets, University of South Carolina, Preprint
Compressed Post Script file ENGL (82 Kb)