Boundary theories of static bulk topological phases matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can quantified/characterized by quantum anomalies, particular when there is a global symmetry. Similarly, Floquet evolutions realize unitary operators at boundaries. In this paper, we discuss characterization such obstructions usin...

1. Let C be the complex field and T be the unit circle { \ £ C : | \ | = 1} . For a non-negative integer m or for m = oo, let OCT) be the space of all m-times continuously differentiable functions on T. (Here we consider T as a C°°-manifold in the natural way. Thus, any / £ C m ( r ) can be identified with an m-times continuously differentiable periodic function f (6) of a real variable 0 with ...

We characterize a special class of unitary operators that preserve orthonormal wavelets. In the process we also prove that symmetric wavelet sets cover the real line.

The method in mathematical logic invented by Schönfinkelf and developed in detail by Curry | is important in that it completely eliminates the variable from the formal presuppositions of logic and mathematics. Constructed according to Schönfinkel's scheme the primitive language of mathematical logic consists only of a few constants; variables, if wanted as a convenience, are introduced afterwar...

In this paper we consider C0-group of unitary operators on a Hilbert C*-module E. In particular we show that if A?L(E) be a C*-algebra including K(E) and ?t a C0-group of *-automorphisms on A, such that there is x?E with =1 and ?t (?x,x) = ?x,x t?R, then there is a C0-group ut of unitaries in L(E) such that ?t(a) = ut a ut*.

This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.