We define multiplication and convolution of distributions and ultradistributions by introducing the notions of evaluation of distributions and integration of ultradistributions. An application is made to an interpretation of the Dirac formalism of quantum mechanics. The role of the Hilbert space of states is played by what is termed a Hermitian orthonormal system, and operators are replaced by the generalized matrices. We describe a simple example of one dimensional free particle and construct explicitly a representation of the Weyl algebra as the generalized matrices.
We study the associativity property of field algebras. After extending the notion of associativity to fields of several variables and developing some structure theorems, we define meromorphic field algebras and relate them to formally rational deformation operads.
We give a necessary and sufficient condition for a primitive of a distribution to have the value at a point in the sense of Łojasiewicz. A formula defining the indefinite integral of a distribution with a basepoint is introduced, and further structural results are discussed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.