Laguerre entire functions and the Lee–Yang property

摘要

Laguerre entire functions are the polynomials of a single complex variable possessing real nonpositive zeros only or their limits on compact subsets of C. These functions are employed to establish a property of isotropic (i.e., O(N)-invariant) probability measures on RN, N∈N. It is called the Lee–Yang property since, in the case N=1, it corresponds to the property of the partition function of certain models of statistical physics, first established by T.D. Lee and C.N. Yang. A class of measures possessing this property is described. Certain connections of the Lee–Yang property with other aspects of the analytic theory of probability measures are discussed.