Abstract. We consider Hankel operators of the form H z k : F m := {f : f is entire and C n |f (z)| 2 e −|z| m < ∞} → L 2 (e −|z| m ). Here k, m, n ∈ N. We show that in the case of one complex dimension the Hankel operators are compact but not Hilbert-Schmidt if m > 2k. PreliminariesThe investigation of Hankel operators on the Bergman space of certain domains Ω has a long history. See, for example, [24] and [25]. Furthermore, there have been some attempts to characterize compactness of Hankel operators on L 2 spaces of entire functions. In [26] the case of essentially bounded symbols is considered. This has the advantage that the corresponding Hankel operator is bounded.There are interesting connections between the theory of partial differential equations and the theory of Hankel operators. In [12] it is shown that the canonical solution operator to ∂ restricted to (0, 1)-forms with coefficients in the spaces of holomorphic functions that are square integrable with respect to the weight function e We want to investigate operators of the formHere P denotes the Bergman projection

In this paper we investigate Hankel operators H f :where A 2 m are general Fock spaces. We will show that H f is not continuous if the corresponding symbol is not a polynomial f = N k=0 b k z k . For polynomial symbols we will give necessary and sufficient conditions for continuity and compactness in terms of N and m. For monomials z k we will give a complete characterization of the Schatten-von Neumann p-class membership for p > 0. Namely in case 2k < m the Hankel operators H z k are in the Schattenvon Neumann p-class iff p > 2m/(m−2k); and in case 2k m they are not in the Schatten-von Neumann p-class.

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Investment decisions are often characterized by uncertainty, irreversibility, and timing flexibility. We use a binomial model to investigate the interdependencies of effects from profit taxation and both an option to delay and an option to abandon on investment decisions. We show that increasing the tax rate can lead to paradoxical tax effects, i.e. it may foster an investor's willingness to invest. By contrast, if we abstract from the abandonment option, such paradoxical effects cannot be identified. Hence, we show that paradoxical tax effects can be caused by an abandonment option. Our results are helpful for investors facing risky investment opportunities and for improving typical valuation approaches.

Earlier literature has pointed to the effectiveness of residual income-type measures based on particular accrual accounting rules such as the relative benefit allocation rule. These performance metrics have been shown to generate desirable managerial incentives when investment decisions are delegated. This paper further attests to the robustness of these measures by extending the result to a sequential adverse selection model with an inherent real option (an option to abandon). In other words, as long as the residual income measures are judiciously constructed, neither private information nor the requirement to selectively exercise an option derails their use in this setting.sequential capital budgeting, residual income, accounting adjustments, sequential adverse selection problem

We consider the canonical solution operator to ∂ restricted to (0, 1)-forms with coefficients in the generalized Fock-spacesf is entire andWe will show that the canonical solution operator restricted to (0, 1)-forms with F m -coefficients can be interpreted as a Hankel-operator. Furthermore we will show that the canonical solution operator is not compact for m ≥ 2. PreliminariesIt is well-known that in many cases compactness of the solution operator to ∂ only depends on the behavior of the solution operator on the closed subspace of forms with holomorphic coefficients (see [7], [8], [13], [16] and [6]).In [6], compactness of the solution operator in the case of bounded convex domains is investigated. It is shown in [6] that compactness of the solution operator for ∂ on (0, 1)-forms implies that the boundary of Ω -in this case Ω is a bounded convex domain -does not contain any analytic variety of dimension greater or equal to 1. The proof only requires the existence of a compact solution operator to ∂ on (0, 1)-forms with holomorphic coefficients. So in the case of bounded convex domains compactness of the solution operator restricted to (0, 1)-forms with holomorphic coefficients implies already compactness of the solution operator on general (0, 1)-forms.A similar situation appears in [16] where the Toeplitz C * -algebra T (Ω) is considered and the relation between the structure of T (Ω) and the ∂-Neumann problem is discussed. Definition 1

Key words Hankel operator, Fock space MSC (2000) 47B35, 32A36In this paper we study generalized Hankel operators of the form H l z k :The investigations in this article extend the ones in [11] and [6], where the special cases l = 0 and l = 1 are considered, respectively. The main result is that the operators H l z k are not bounded for l < k − 1. The proof relies on a combinatoric argument and a generalization to general conjugate holomorphic L 2 symbols, generalizing arguments from [6], seems possible and is planned for future work.

ABSTRACT:Politicians and tax practitioners often claim that tax uncertainty negatively affects investment. In many countries, firms can request fee-based Advance Tax Rulings (ATRs) to mitigate tax uncertainty. We analyze theoretically the circumstances under which investors request ATRs, how tax authorities should price them and how they can affect investment. We assume that tax authorities integrate investors' reasoning into their decisions. We determine the optimal fee tax authorities should charge. We find that in special cases this fee is prohibitively high, thus firms will refrain from requesting ATRs. However, we find that revenue-maximizing tax authorities offer ATRs if the ruling enables them either to significantly reduce their tax audit costs or to increase the probability of detecting ambiguous tax issues. Under certain circumstances, ATRs may effectively foster investment and potentially benefit both the tax authorities and taxpayers. Our results provide new explanations for why taxpayers that face high levels of tax uncertainty often do not request ATRs, even when the fee is rather low. Our results also hold when the tax authority maximizes social wealth instead of its revenues. Regulatory changes in ATR requirements might serve as a natural quasi-experiment for an empirical study of our predictions regarding investment decisions.