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.
Corso R. (2019). A Lebesgue-type decomposition for non-positive sesquilinear forms. ANNALI DI MATEMATICA PURA ED APPLICATA, 198(1), 273-288 [10.1007/s10231-018-0773-5].
A Lebesgue-type decomposition for non-positive sesquilinear forms
Corso R.
2019-01-01
Abstract
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.
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