Sesión Análisis Funcional y ComplejoCarlson’s formula on the boundary of the half-plane
Florencia Marchesano
IMaS (UBA-CONICET) - Depto. de Matemática, Facultad de Cs. Exactas y Naturales, UBA, Argentina - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
A classic result due to Fritz Carlson (1922) relates the quadratic sum of the coefficients of a bounded Dirichlet series in a half-plane to its integral means on vertical lines within that half-plane. In 2004, Hedenmalm, revisiting Carlson’s ideas, posed a natural question: can this formula be extended to the boundary of the half-plane? In 2007, Saksman and Seip provided a counterexample, thereby answering Hedenmalm’s question in the negative. In this talk, we analyze some additional hypotheses on the frequencies and coefficients of a series that guarantee the validity of Carlson’s formula on the boundary of the half-plane.
Trabajo en conjunto con: Daniel Carando (Universidad de Buenos Aires - CONICET).