A Lebesgue-type decomposition of a (not necessarily non-negative) sesquilinear form with respect to a non-negative one is studied. This decomposition consists of a sum of three parts: two are dominated by an absolutely continuous form and a singular non-negative one, respectively, and the latter is majorized by the product of an absolutely continuous and a singular non-negative forms. The Lebesgue decomposition of a complex measure is given as application.
|Number of pages||16|
|Journal||Annali di Matematica Pura ed Applicata|
|Publication status||Published - 2019|
All Science Journal Classification (ASJC) codes
- Applied Mathematics