The initial mass function describes the distribution of masses for a population of stars and substellar objects when they are born. It defines the evolution of a population of stars and provides constrains on the star formation theory. The determination of the initial mass function in the substellar regime is still an open question in Astrophysics. Brown dwarfs do not have enough mass to sustain hydrogen fusion. As a consequence, mass and age are degenerate for these objects. An older high mass object may be indistinguishable from a younger low mass object. In my PhD thesis, through the characterization of brown dwarfs using several observational methods, I work towards solving the general problem of constraining the substellar initial mass function.

In my first project, I calculated trigonometric parallaxes of a sample of six cool brown dwarfs. I determined the luminosity for our objects and I found that one of them might be a brown dwarf binary. In my second project, I confirmed the youth of seven brown dwarfs (ages between 1 and 150 Myr) using spectroscopic data.In the last project of this PhD thesis, I aimed to refine the brown dwarf binary fraction using spectroscopic data in the optical and in the near infrared for 22 brown dwarfs. I found six new brown dwarf binary candidates, two of them were previously known.

The determination of distances, ages and the refinement of the brown dwarf binary fraction in this PhD thesis contribute to the determination of the initial mass function. In the next years, the Gaia satellite, the James Webb Space Telescope and the E-ELT will provide new data, allowing the discovery of new brown dwarf binaries, the constraining of atmospheric and evolutionary models, and the refinement of the initial mass function.