Symmetry Minimizers and Meromorphic Continuation of Dynamical Zeta Functions with continuity Envelopes

Abstract

We study the symmetry of minimizers for a large class of non-local variational problems. We study the identities that lead to symmetry results, the functional that can be considered and the functional spaces that can be used. Then we use the method to prove the symmetry of minimizers for a class of variational problems involving the fractional power of Laplacian. We describe a method to prove meromorphic continuation of dynamical zeta function to the entire complex plane under the condition that the corresponding partition function given, that is, a dynamical trace formula from a family of transfer operators. Further, we give general condition for the partition function associated with general spin chains to be of this type. We show a Maury type result for operator spaces. We study continuity envelopes in space of generalized smoothness and show sharp embedding assertions in some limiting situations.