Research

• Functional analysis: Measure and integration in functional spaces, Toeplitz operators, Integral operators, Aggregation operators
• Applied Mathematics: Uncertainty-based information theory (applied to Sampling techniques in Statistics), Formal Laurent series of more variables of finite rank (applied to Tone systems in Music)

Achievements and principal contributions

• results in integration of vector functions with respect to the operator valued measure in vector spaces equipped with additional structures (topological, bornological, order); in particular, a generalization of the Dobrakov theory of integration to complete bornological locally convex spaces
• creation of a unifying mathematical theory of tone systems based on geometrical nets (equivalently, formal Laurent series of more variables of finite rank)
• creation of an approach to the statistical sampling techniques theory based on the uncertainty-based information theory

Leader of granted projects

• 2011--2013 Integral and differential operators and their algebras,   Grant VEGA 2/0035/11
• 2008--2010 Toeplitz operators and their applications,   Grant VEGA 2/0097/08
• 2005--2007 Mathematical Methods of oscillatory systems and uncertainty,  Grant VEGA 2/5065/05
• 2007--2009 Integration in abstract structures, Grant SAV Bratislava - CNR Roma
• 2005--2007 Mathematical Methods of oscillatory systems and uncertainty,  Grant VEGA 2/5065/05
• 2001--2003 Integration in vector spaces equipped with additional structures, Grant SAV Bratislava - CNR Roma
• 1998--2000 Tone systems, Grant VEGA 2/5126/98