The Segal--Bargmann transform for odd-dimensional hyperbolic spaces

We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.Comment: To appear in Mathematic

Coherent states for a 2-sphere with a magnetic field

We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on earlier work in the nonmagnetic case, we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S^2. They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certain heat kernel. These coherent states are not of Perelomov type, but rather are constructed according to the "complexifier" approach of T. Thiemann. We describe the Segal--Bargmann representation associated to the coherent states, which is equivalent to a resolution of the identity.Comment: 23 pages. To appear in Journal of Physics A, Special Issue on Coherent State

Serre Duality, Abel's Theorem, and Jacobi Inversion for Supercurves Over a Thick Superpoint

The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1|q over a finite-dimensional local supercommutative C-algebra. The theorem is proved by establishing a compatibility of Serre duality for the supercurve with Poincare duality on the reduced curve. We include an elementary algebraic proof of the requisite form of Serre duality, closely based on the account of the reduced case given by Serre in Algebraic Groups and Class Fields, combined with an invariance result for the topology on the dual of the space of repartitions. Our Abel map, taking Cartier divisors of degree zero to the dual of the space of sections of the Berezinian sheaf, modulo periods, is defined via Penkov's characterization of the Berezinian sheaf as the cohomology of the de Rham complex of the sheaf D of differential operators, as a right module over itself. We discuss the Jacobi inversion problem for the Abel map and give an example demonstrating that if n is an integer sufficiently large that the generic divisor of degree n is linearly equivalent to an effective divisor, this need not be the case for all divisors of degree n.Comment: 14 page

The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L^2 space of meromorphic functions. For general functions, we give an inversion formula for the Segal-Bargmann transform, involving integration against an "unwrapped" version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.Comment: 28 pages. Minor corrections made. To appear in J. Functional Analysi

FIRM EFFICIENCY AND INFORMATION TECHNOLOGY USE: EVIDENCE FROM U.S. CASH GRAIN FARMS

We implement stochastic frontier analysis techniques to show the effects of information technology use on firm efficiency. Results from a sample of 1,865 U.S. cash grain farms reveals that information technology use within the farm business moved farms significantly towards the efficiency frontier. Also moving farms towards the efficiency frontier were the use of written long-term plans, advanced input acquisition strategies, and increased farm labor hours relative to total labor hours. In contrast, an increase in the debt to asset ratio was associated with movements away from the efficiency frontier.Crop Production/Industries,

DISTRIBUTIONAL ANALYSIS OF U.S. FARM HOUSEHOLD INCOME

expenditures, farm safety net, household income, poverty, stochastic dominance, wealth, Consumer/Household Economics,

Short Time Behavior of Hermite Functions on Compact Lie Groups

AbstractLetpt(x) be the (Gaussian) heat kernel on Rnat timet. The classical Hermite polynomials at timetmay be defined by a Rodriguez formula, given byHα(−x, t)pt(x)=αpt(x), whereαis a constant coefficient differential operator on Rn. Recent work of Gross (1993) and Hijab (1994) has led to the study of a new class of functions on a general compact Lie group,G. In analogy with the Rncase, these “Hermite functions” onGare obtained by the same formula, whereinpt(x) is now the heat kernel on the group, −xis replaced byx−1, andαis a right invariant differential operator. Let g be the Lie algebra ofG. Composing a Hermite function onGwith the exponential map produces a family of functions on g. We prove that these functions, scaled appropriately int, approach the classical Hermite polynomials at time 1 asttends to 0, both uniformly on compact subsets of g and inLp(g, μ), where 1⩽p<∞, andμis a Gaussian measure on g. Similar theorems are established whenGis replaced byG/K, whereKis some closed, connected subgroup ofG

Taxing Retirement Income: Nonqualified Annuities and Distributions from Qualified Accounts

This paper explores the current tax treatment of non-qualified immediate annuities and distributions from tax-qualified retirement plans in the United States. First, we describe how immediate annuities held outside retirement accounts are taxed. We conclude that the current income tax treatment of annuities does not substantially alter the incentive to purchase an annuity rather than a taxable bond. We nevertheless find differences across different individuals in the effective tax burden on annuity contracts. Second, we examine an alternative method of taxing annuities that would avoid changing the fraction of the annuity payment that is included in taxable income as the annuitant ages, but would still raise the same expected present discounted value of revenues as the current income tax rule. We find that a shift to a constant inclusion ratio increases the utility of annuitants, and that this increase is greater for more risk averse individuals. Third, we examine how payouts from qualified accounts are taxed, focusing on both annuity payouts and minimum distribution requirements that constrain the feasible time path of nonannuitized payouts. We describe briefly the origins and workings of the minimum distribution rules and we also provide evidence on the fraction of retirement assets potentially affected by these rules.