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math-ph2012★ 14 cited
The initial value problem for ordinary differential equations with infinitely many derivatives
Przemyslaw Gorka, Humberto Prado, Enrique G. Reyes
We study existence, uniqueness and regularity of solutions for ordinary differential equations with infinitely many derivatives such as (linearized versions of) nonlocal field equa…
math-ph2012★ 3 cited
Sobolev spaces on locally compact abelian groups
Przemysław Górka, Enrique G. Reyes
Motivated by a class of nonlinear equations of interest for string theory, we introduce Sobolev spaces on arbitrary locally compact abelian groups and we examine some of their prop…