Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time regularization that may involve a Wiener measure concentrated on continuous phase space paths. The introduction of constraints is both natural and economica...

A semidiscrete multiplier is an operator between a space of functions or distributions on a locally compact Abelian group G on the one hand, and a space of sequences on a discrete subgroup H of G on the other hand, with the property that it commutes with shifts by H. We describe the basic form of such operators and show a number of representation theorems for classical spaces like Lp, C0, etc. ...

Given a group G and an integer n ≥ 2 we construct a new group e K(G, n). Although this construction naturally occurs in the context of finding new invariants for complex algebraic surfaces, it is related to the theory of central extensions and the Schur multiplier. A surprising application is that Abelian groups of odd order possess naturally defined covers that can be computed from a given cov...

A,(T) = [L9(T) ® LQ(T)]IK where K is the kernel of the convolution operator c:Lp(S>LQ(T)->C0(T) by (f®g)(y)(f* g)(y)-4*(r) is the /?-Fourier algebra which was introduced by Figa-Talamanca in [6] where it was shown that ^ ( T ) * isisometrically isomorphic to MP(T), the bounded, translation invariant, linear operators on LP(T), Herz [11] showed that AP(V) is a Banach algebra under pointwise mult...

We prove norm estimates for the difference of resolvents operators and their discrete counterparts, embedded into continuum using biorthogonal Riesz sequences. The are given in operator on square integrable functions, depend explicitly mesh size operators. a sum Fourier multiplier multiplicative potential. multipliers include fractional Laplacian pseudo-relativistic free Hamiltonian. potentials...

A result of Gilbert shows that every completely bounded multiplier f of the Fourier algebra A(G) arises from a pair of bounded continuous maps α, β : G → K, where K is a Hilbert space, and f(s−1t) = (β(t)|α(s)) for all s, t ∈ G. We recast this in terms of adjointable operators acting between certain Hilbert C∗-modules, and show that an analogous construction works for completely bounded left mu...

Suppose u is the solution of the initial value problem utt −∆xu = 0, (x, t) ∈ R × [0,∞); u(x, t=0) = f(x), ut(x, t=0) = g(x), x ∈ R. Suppose n ≥ 1 is odd, f and g are supported in a ball B with boundary S, and one of f or g is zero. We derive identities relating the norm of f or g to the norm of the trace of u on S× [0,∞). These identities are derived using integral geometric and multiplier met...

we observe that the transform, with respect to any operator of 6r, of the commutators formed with t and the operators of G is the product of two such commutators. All of these commutators must, therefore, form a group which is transformed into itself by G. When t transforms G into itself the given commutators generate the smallest self-conjugate subgroup of G which has the property that all of ...