Objective: This study investigates the impact of maxillary advancement (Le Fort Iosteotomy) on consonant proficiency in patients with cleft lip and palate (CLP) and explores how these patients and lay people perceive their speech 1 year post Le Fort I osteotomy. Design: Retrospective group study before and after treatment. Participants: All patients with CLP who had undergone Le Fort I osteotomy for maxillary retrognathia between 2007 and 2010 at Karolinska University Hospital, Sweden (n = 21). Six patients were excluded due to additional malformations and missing data. Two experienced speech and language pathologists assessed consonant proficiency, and speech accuracy was determined by lay listeners from pre- and postoperative standardized audio recordings. The patients' satisfaction with speech postoperatively was collected from medical records. Main Outcome Measures: Percentage of oral consonants correct and acoustic analysis of /s/, lay listeners' opinion, and patients' satisfaction with speech. Results: One year postoperation, 11 of the 15 patients had improved articulation, especially on the /s/-sound, without speech intervention. The mean percentage of oral consonants correct before treatment (82%) was significantly improved later (95%; P > .01). This assessment was supported by the patients' satisfaction with speech. However, lay listeners' opinion on accuracy was inconsistent. Length of maxillary advancement or change in occlusion did not correlate with change in articulation. Conclusion: Maxillary advancement performed to normalize occlusion and facial profile improved consonant proficiency in patients with CLP 1 year postoperation. Lay listeners' and patients' perceptions of speech need further exploration.

We provide an abstract approach to approximation with a wide range of regularity classes X in spaces of pseudocontinuable functions Kp Θ, where Θ is an inner function and p > 0. More precisely, we demonstrate a general principle, attributed to A. Aleksandrov, which asserts that if a certain linear manifold X is dense in Kq Θ for some q > 0, then X is in fact dense in Kp Θ for all p > 0. Moreover, for a rich class of Banach spaces of analytic functions X, we describe the precise mechanism that determines when X is dense in a certain space of pseudocontinuable functions. As a consequence, we obtain an extension of Aleksandrov's density theorem to the class of analytic functions with uniformly convergent Taylor series. 

We characterize the model spaces symbolscript in which functions with smooth boundary extensions are dense. It is shown that such approximations are possible if and only if the singular measure associated to the singular inner factor of 0 is con-centrated on a countable union of Beurling-Carleson sets. In fact, we use a duality argument to show that if there exists a restriction of the associated singular meas-ure which does not assign positive measure to any Beurling-Carleson set, then even larger classes of functions, such as Holder classes and large collections of analytic Sobolev spaces, fail to be dense. In contrast to earlier results on density of functions with continuous extensions to the boundary in symbolscript and related spaces, the existence of a smooth approximant is obtained through a constructive method.

For the class of de Branges-Rovnyak spaces H(b) of the unit disk D defined by extreme points b of the unit ball of H infinity, we study the problem of approximation of a general function in H(b) by a function with an extension to the unit circle T of some degree of smoothness, for instance satisfying Holder estimates or being differentiable. We will exhibit connections between this question and the theory of subnormal operators and, in particular, we will tie the possibility of smooth approximations to properties of invariant subspaces of a certain subnormal operator. This leads us to several computable conditions on b which are necessary for such approximations to be possible. For a large class of extreme points b we use our result to obtain explicit necessary and sufficient conditions on the symbol b which guarantee the density of functions with differentiable boundary values in the space H(b). These conditions include an interplay between the modulus of b on T and the spectrum of its inner factor.

It is well known that for any inner function θ defined in the unit disk D, the following two conditions: (i) there exists a sequence of polynomials {p_n}_n such that lim_n→∞θ(z)p_n(z)=1 for all z ∈ D and (ii) sup_n∥θp_n∥_∞<∞, are incompatible, i.e., cannot be satisfied simultaneously. However, it is also known that if we relax the second condition to allow for arbitrarily slow growth of the sequence {θ(z)p_n(z)}_n as |z|→1, then condition (i) can be met for some singular inner function. We discuss certain consequences of this fact which are related to the rate of decay of Taylor coefficients and moduli of continuity of functions in model spaces K_θ. In particular, we establish a variant of a result of Khavinson and Dyakonov on nonexistence of functions with certain smoothness properties in K_θ, and we show that the classical Aleksandrov theorem on density of continuous functions in K_θ is essentially optimal. We consider also the same questions in the context of de Branges–Rovnyak spaces H(b) and show that the corresponding approximation result also is optimal.

We study the classical problem of identifying the structure of P2(μ), the closure of analytic polynomials in the Lebesgue space L2(μ) of a compactly supported Borel measure μ living in the complex plane. In his influential work, Thomson [Ann. of Math. (2) 133 (1991), pp. 477-507] showed that the space decomposes into a full L2-space and other pieces which are essentially spaces of analytic functions on domains in the plane. For a family of measures μ supported on the closed unit disk D which have a part on the open disk D which is similar to the Lebesgue area measure, and a part on the unit circle T which is the restriction of the Lebesgue linear measure to a general measurable subset E of T, we extend the ideas of Khrushchev and calculate the exact form of the Thomson decomposition of the space P2(μ). It turns out that the space splits according to a certain natural decomposition of measurable subsets of T which we introduce. We highlight applications to the theory of the Cauchy integral operator and de Branges-Rovnyak spaces.