Plane potential theory, special functions, analytic functions of one complex variable, approximation theory, inequalities.
Main publications:
D. Karp, “Square summability with geometric weight for classical orthogonal expansions”, Advances in Analysis, Proceedings of the 4th International ISAAC Conference, eds. H. G. W. Begehr et al., 2005, 407–421
D. Karp, “Hypergeometric reproducing kernels and analytic continuation from a half-line”, Integral Transforms and Special Functions, 14:6 (2003), 485–498
D. Karp, “Capacity of a condenser whose plates are circular arcs”, Complex Variables and Elliptic Equations, 50:2 (2005), 103–122
D. Karp and S. M. Sitnik, “Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity”, Journal of Computational and Applied Mathematics, 205:1 (2007), 186–206
D. Karp and S. M. Sitnik, “Inequalities and monotonicity of ratios for generalized hypergeometric function”, Journal of Approximation Theory, 2009, no. 161, 337–352
Asena Çetinkaya, Dmitrii Karp, Elena Prilepkina, “Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities”, SIGMA, 17 (2021), 098, 25 pp.
D. B. Karp, E. G. Prilepkina, “An inverse factorial series for a general gamma ratio and related properties of the Nørlund–Bernoulli polynomials”, Zap. Nauchn. Sem. POMI, 458 (2017), 135–158; J. Math. Sci. (N. Y.), 234:5 (2018), 680–696
Dmitrii Karp, Elena Prilepkina, “Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring”, SIGMA, 12 (2016), 052, 23 pp.
D. B. Karp, “Normalized incomplete beta function: log-concavity in parameters and other properties”, Zap. Nauchn. Sem. POMI, 440 (2015), 138–161; J. Math. Sci. (N. Y.), 217:1 (2016), 91–107
S. I. Kalmykov, D. B. Karp, “On logarithmic concavity of series in gamma ratios”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 6, 70–77; Russian Math. (Iz. VUZ), 58:6 (2014), 63–68
D. B. Karp, “Representations and inequalities for generalized hypergeometric functions”, Zap. Nauchn. Sem. POMI, 429 (2014), 121–139; J. Math. Sci. (N. Y.), 207:6 (2015), 885–897
D. B. Karp, “Positivity of Toeplitz determinants formed by rising factorial series and properties of related polynomials”, Zap. Nauchn. Sem. POMI, 404 (2012), 184–198; J. Math. Sci. (N. Y.), 193:1 (2013), 106–114
D. B. Karp, “Turan's inequalities for the Kummer function in a simultaneous shift of the two parameters”, Zap. Nauchn. Sem. POMI, 383 (2010), 110–125; J. Math. Sci. (N. Y.), 178:2 (2011), 178–186
V. N. Dubinin, D. B. Karp, V. A. Shlyk, “Selected problems of geometrical theory of functions and potential theory”, Dal'nevost. Mat. Zh., 8:1 (2008), 46–95
D. B. Karp, “Criterion of square summability with geometric weight for Jacobi expansions”, Dal'nevost. Mat. Zh., 1:1 (2000), 16–27
1994
13.
D. B. Karp, “Fractional Hankel transformation and its applications in
mathematical physics”, Dokl. Akad. Nauk, 338:1 (1994), 10–14; Dokl. Math., 50:2 (1995), 179–185
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