U.S.-Romania Mathematics Research: Factorization, Extension, and Interpolation Problems for Operator-valued Functions on Groups

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The goal of this U.S.-Romanian mathematics project between Mihai Bakonyi of Georgia State University and Dan G. Timotin of the Romanian Academy's Institute of Mathematical Sciences is to advance our knowledge of positive definite functions on groups, an area of interest in noncommutative harmonic analysis. This will be accomplished by considering two classes of groups, first, totally ordered abelian groups and second, finitely generated nonabelian free groups. Building on the U.S. participants' strengths in factorization and extension problems and the Romanian side's in interpolation and operator generalizations, the team intends to examine: 1) factorization of positive definite operator-valued functions, 2) extensions of partially positive definite operator-valued functions on finitely generated free groups and 3) interpolation of operator-valued functions on free groups. Results are expected to lead to a more unified theoretical framework for multivariable operator theory and related areas of operator algebras. Success would enhance future applications in system theory and electrical engineering. This mathematics project fulfills the program objective of advancing scientific knowledge by enabling experts in the United States and Central Europe to combine complementary talents and share research resources in areas of strong mutual interest and competence. Broader impacts include the introduction of U.S. and Romanian students to the international community of people working on multivariable operator theory through collaborative work at partner institutions and direct involvement in the project's advanced data analysis and modeling techniques.