Recent Publications

BOOKS and BOOKCHAPTERS

1. Piskarev S.I., Vasiliev V.V. Differential Equations in Banach

Spaces I. Semigroup Theory. Moscow State University Publish House

(in Russian), 1996, 164 p.

2. Piskarev S.I., Vasiliev V.V. Differential Equations in Banach

Spaces. Theory of Cosine Operator-Functions. ( in preparation) (in Russian).

3. Vasiljev V.V., Krein S.G., Piskarev S.I. Semigroups of

operators, cosine operator functions and linear differential equations.

Progress in Science and Technology. Mathematical analysis, Vol. 28,

p. 87 - 204, 1990.

ARTICLES in JOURNALS and PROCEEDINGS

Piskarev S., Piskunov D. Application of the method of conjugate gradients to adaptive spatial filtering. Soviet Journal of Comm. Technology and Electronics., 1990, 35, N 5, p. 17 - 25.

Piskarev S. Approximation of positive $C_0$-semigroups. Differen. Uravnenija, 27, N 7, p.1245 - 1250, 1991.

Piskarev S. Compactness properties in the theory of the cosine operator functions. Mathemat. Zametki, 1992, Vol. 51, N 5, p. 151 - 153.

Crouzeix M., Larsson S., Piskarev S., Thomee V. The stability of rational approximations of analytic semigroups. BIT, 1993, Vol. 33, p. 74 - 84.

Piskarev S. Rational approximations of analytic semigroups. Proc. of 3rd International Workshop-Conference on Evolution Equations, Control Theory and Biomathematics. Belgium, "Han-sur-Lesse, October 20-26, 1991", p. 467-471, Marcel Dekker, Inc., 1993.

Piskarev S., Shaw S.-Y. Multiplicative perturbations of $C_0$-semigroups and applications to step responses and cumulative outputs. J. Funct. Anal., 1995, 128, N2, p. 315-340.

Piskarev S., Shaw S.-Y. On some properties of step responses and cumulative outputs. Chinese J. Math., 1994, Vol. 22, No. 4, p. 321-336.

Piskarev S., Shaw S.-Y. Asymptotic behavior of some functions related to $C_0$-semigroups of operators. Saitama J. Math., 1994, 12, p. 7 - 12.

Piskarev S., Shaw S.-Y. Perturbation and Comparison of Cosine Operator Functions. Semigroup Forum, 1995, 51, p.225-246.

Piskarev S. On approximation of perturbed $C_0$-semigroups. Differential Equations (in Russian), 1994, 30, 2, p. 339-341.

Piskarev S., Shaw S.-Y. Perturbation of cosine operator functions by step response and cumulative output, to appear in the Proceedings of the Conference

on Evolution Equations, University of Strathclyde, July 25-29, 1994.

deLaubenfels R., Piskarev S. The growth rate of cosine families. J. Math. Anal. and Appl., 1995, 196, p. 442-451.

Ergenc T., Karasozen B., Piskarev S. Approximation for semilinear Cauchy problems involving second order equations in separable Banach spaces. Nonlinear Anal. Theory, Meth. and Appl., 1997, Vol 28, p. 1157-1165.

Piskarev S., Shaw S.-Y. On certain operator families related to cosine operator functions. Taiwanese J. Math., 1997, 1, p. 527-546.

Guidetti D., Piskarev S. On maximal regularity stability of difference schemes for parabolic equations in $C^\theta(\Omega)$ spaces. Preprint, Department of mathematics, University of Bologna, N 8, 1997.

Bobylev N.A., Kim J.K., Korovin S.K. and Piskarev S. Semidiscrete approximations of semilinear periodic problems in Banach spaces. Nonlin. Anal. Meth. Theory and Applications, 1998, Vol. 33, No.5, p. 473-482.

Guidetti D., Piskarev S. "On maximal regularity of Crank-Nicolson schemes for parabolic equations in $C^{\theta}(\overline \Omega)$ space". Proceedings of International Conference "Function spaces. Differential operators. Problems of mathematical education", Vol.2, p.217 - 222, Moscow: RUDN, 1998.

Guidetti D., Piskarev S., "Stability of Rothe's scheme and maximal regularity for parabolic equations in $C^{\theta}(\overline \Omega)$", in "Progress in

partial Differential Equations", Pont-\'a-Mousson 1997, vol. 1 (ed. H. Amann, C. Bandle, M. Chipot, F. Conrad, I. Shafrir), Pitman Research Notes in Math. 383 (1998).

Ahues M., Piskarev S. Spectral approximation of weakly singular integral operators. I: Convergence theory. Integral methods in science and engineering. Vol. II: Approximation methods. Proceedings of the 4-th international conference, IMSE '96, Oulu, Finland, June 17-20, 1996. Harlow: Longman. Pitman Res. Notes Math. Ser. 375, 35-39 (1997).

Guidetti D. Piskarev S. Stability of the Crank-Nicolson scheme and maximal regularity for parabolic equations in $C\sp \theta(\overline\Omega)$ spaces. Numer. Funct. Anal. Optim. 20 (1999), no. 3-4, 251--277.

Chyan D.-K. Shaw S.-Y., Piskarev S. On maximal regularity and semivariation of cosine operator functions. (English. English summary) J. London Math. Soc. (2) 59 (1999), no. 3, 1023--1032.

Burrage K., Piskarev S. Stochastic methods for ill-posed problems. BIT, 2000, Vol. 40, N 2, pp. 226 - 240.

Vasilev V.V., Piskarev S.I. Bibliography on Differential Equations in Abstract Spaces. Moscow State University, 2001, Electronic journal.

http://www.srcc.msu.ru/num_anal/list_wrk/page_5u.htm

PostScript (1115,2 Kb) PostScript.zip (336,1 Kb)

Palencia C., Piskarev S. On the Multiplicative perturbations of $C_0$-groups and $C_0$-cosine operator functions. Semigroup Forum, 2001, Vol. 63, N 2, p. 127-152.

van Casteren J., Piskarev S. and Shaw S.-Y. Discretisation of $C$-semigroups. Proceedings of the Conference on Inverse and ill-posed problems. Moscow State University, Moscow , 1998, p.18 .

Guidetti D., Karasozen B. and Piskarev S. Approximation of abstract differential equations. 2001, Electronic journal. To get the whole paper send the command "get evolve-l 01-00036" to the following e-mail address:

listserv@uni-karlsruhe.de

Instead you may get the paper at

"http://ma1serv.mathematik.uni-karlsruhe.de/evolve-l/index.html"

Ashyralyev A., Piskarev S.I. and Weis L. On well-posedness of difference schemes for abstract parabolic equations in $L^p([0,T];E)$ spaces. Proc. Voronezh Spring School "Pontrjagin's lectures-XIII", p. 9-10, 2002.

PUBLICATIONS SUBMITTED

van Casteren J., Piskarev S. and Shaw S.-Y. Discretisation of $C$-semigroups. Subm. to Inverse and Ill-posed Problems.

Kantorovitz S., Piskarev S. Mean stability of semigroups and cosine operator functions. To appear in Taiwanese Journal of Mathematics.

Jefferies B., Piskarev S. Tauberian theorems for semigroups. To appear in Proceedings of Maratea conference.

Jefferies B., Piskarev S. Tauberian theorems for cosine operator functions. Submitted to Proceedings of Steklov Institute.

Guidetti D., Piskarev S. Some remarks on real interpolation and finite differences. Submitted to Abstract and Applied Analysis.

Takenaka T., Piskarev S. Local $C$-cosine families and local integrated cosine families. Subm. To Taiwan J. of Math.

Ashyralyev A., Piskarev S., Weis L. On well-posedness of difference schemes for abstract parabolic equations in $L^p([0,T];E)$ spaces. Subm. To Numerical Functional Analysis and Optimization.

Li Miao , Guo B.-Z. and Piskarev S. Compactness and norm continuity of the difference of two cosine functions. Subm. To Taiwaness Journal of Mathematics.

Guidetti D., Karasozen B. and Piskarev S. Approximation of abstract differential equations. Subm. To VINITI survey.