Research/publications

I work mainly in operator related function theory and time-frequency analysis. I am involved in the study of spaces of analytic functions, such as Hardy spaces, de Branges-Rovnyak spaces, Paley-Wiener spaces, de Branges spaces of entire functions, model subspaces of Hardy spaces, Bergman spaces, Dirichlet spaces, and Fock spaces. This topic connects complex analysis with neighboring fields such as operator theory and harmonic analysis as well as with applied disciplines such as mathematical physics and signal analysis. Some papers of mine study the spanning properties of systems of functions and can be viewed as belonging to time-frequency analysis. A project that has evolved for some years, is the development of a theory of Hardy spaces of Dirichlet series modeled on the classical theory of Hardy spaces; this topic interacts with function theory on polydiscs and analytic number theory. Occasionally my work is of a purely operator theoretic nature, studying properties of objects such as Toeplitz and Hankel operators.

Below I have listed my publications since approximately 2004 according to a division into four main topics. For older papers, I refer to my publications in MathSciNet.

Time-frequency analysis and spanning properties of systems of functions

• Karlheinz Gröchenig, Gitta Kutyniok, and Kristian Seip, Landau's necessary density conditions for LCA groups, J. Funct. Anal. 255 (2008), 1831–1850.
• Gerard Ascensi, Yurii Lyubarskii, and Kristian Seip, Phase space distribution of Gabor expansions , Appl. Comp. Harm. Anal. 26 (2009), 277-282.
• Jordi Marzo and Kristian Seip, The Kadets 1/4 theorem for polynomials, Math. Scand. 104 (2009), 311-318.
• Yurii Belov, Tesfa Mengestie, and Kristian Seip, Unitary discrete Hilbert transforms, J. Anal. Math. 112 (2010), 383-393.
• Yurii Belov, Tesfa Mengestie, and Kristian Seip, Discrete Hilbert transforms on sparse sequences, arXiv:0912.2899v1, 2009; Proc. London Math. Soc. 103 (2011), 73-105. DOI: 10.1112/plms/pdq053.
• Kristian Seip, Interpolation and sampling in small Bergman spaces, arXiv:1106.3847v2, 2011; Collect. Math., to appear; DOI: 10.1007/s13348-011-0054-8.

Dirichlet series and function theory in polydiscs

• Jan-Fredrik Olsen and Kristian Seip, Local interpolation in Hilbert spaces of Dirichlet series, Proc. Amer. Math. Soc. 136 (2008), 203--212.
• Eero Saksman and Kristian Seip, Integral means and boundary limits of Dirichlet series, Bull. London Math. Soc. 41 (2009), 411-422; DOI 10.1112/blms/bdp004.
• Kristian Seip, Interpolation by Dirichlet series in $H^\infty$, Advances in the Mathematical Sciences, Series 2, Vol. 26, Amer. Math. Soc., Providence, R.I., 2009, pp. 153-164.
• Joaquim Ortega-Cerdà, Andreas Defant, Leonhard Frerick, Myriam Ounaïes, and Kristian Seip, The Bohnenblust--Hille inequality for homogeneous polynomials is hypercontractive, Ann. of Math. 174 (2011), 485--497; DOI 10.4007/annals.2011.174.1.13.
• Jordi Marzo and Kristian Seip, $L^\infty$ to $L^p$ constants for Riesz projections, Bull. Sci. Math. 135 (2011), 324--331.
• Joaquim Ortega-Cerdà and Kristian Seip, A lower bound in Nehari's theorem on the polydisc, J. Anal. Math., to appear.

Operator Theory

• Andreas Hartmann, Donald Sarason, and Kristian Seip, Surjective Toeplitz operators, Acta Sci. Math. (Szeged) 70 (2004), 609--621.
• Kristian Seip and El Hassan Youssfi, Hankel operators on Fock spaces and related Bergman kernel estimates, arXiv:1011.2408v1, 2010; J. Geom. Anal., to appear; DOI 10.1007/s12220-011-9241-9.
• Omar El-Fallah, Karim Kellay, and Kristian Seip, Cyclicity of singular inner functions from the corona theorem, arXiv:1012.5822v1, 2010; J. Inst. Math. Jussieu, to appear.

Negative refraction and Hardy spaces

• Kristian Seip and Johannes Skaar, An extremal problem related to negative refraction, Skr. K. Nor. Videns. Selsk. 3 (2005), 1--8.
• Johannes Skaar and Kristian Seip, Bounds for the refractive indices of metamaterials, Journal of Physics D: Applied Physics 39 (2006), 1226-1229.
• Øyvind Lind-Johansen, Kristian Seip, and Johannes Skaar, The perfect lens on a finite bandwidth, J. Math. Phys. 50 (2009). (Copyright (2009) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the authors and the American Institute of Physics. The online version of this paper may be found at http://link.aip.org/link/?JMP/50/012908.)