Dense definiteness and boundedness of composition operators in L^2-spaces via inductive limits

In this paper, we specify what functions induce the bounded composition operators on a reproducing kernel Hilbert space (RKHS) associated with an analytic positive definite function defined on Rd. We prove that only affine transforms can do so in a certain large class of RKHS. Our result covers not only the Paley-Wiener space on the real line, studied in previous works, but also much more general RKHSs corresponding to analytic positive definite functions, where existing methods do not work. Our method only relies on intrinsic properties of the RKHSs, and we establish a connection between the behavior of composition operators and asymptotic properties of the greatest zeros of orthogonal polynomials on a weighted L2-space on the real line. We also investigate the compactness of the composition operators and show that any bounded composition operators cannot be compact in our situation.

In this paper, we investigate the boundedness of composition operators defined on a quasi-Banach space continuously included in the space of smooth functions on a manifold. We prove that the boundedness of a composition operator strongly limits the behavior of the original map, and it provides an effective method to investigate the properties of composition operators using the theory of dynamical system. Consequently, we prove that only affine maps can induce bounded composition operators on any quasi-Banach space continuously included in the space of entire functions of one variable if the function space contains a nonconstant function. We also prove that any polynomial automorphisms except affine transforms cannot induce bounded composition operators on a quasi-Banach space composed of entire functions in the two-dimensional complex affine space under several mild conditions.

Historically, an adequate surgical procedure has been the most effective means of treating the majority of primary musculoskeletal sarcomas, and amputation has figured prominently in the surgical armamentarium. 4, 7, 9, 19, 21, 29, 41 The recent evidence that certain chemotherapeutic agents may have significant anti-sarcoma activity 2, 15, 17, 38 and coincident technical advances in irradiation therapy, radiographic localization, and reconstructive surgery have fostered enthusiastic interest in extremity-saving treatments. Almost all such treatments emphasize limb salvage as an alternative to amputation and are usually performed under a protective cloak of adjunctive chemotherapy, irradiation or immunoactive agents. 20, 23, 24, 30, 37, 39 Since neither chemotherapy nor irradiation therapy alone has been shown to assure long-term local control of bulk disease, surgical intervention remains an essential step in the overall management of musculoskeletal sarcomas. 3, 9, 17, 18, 29 Questions concerning the magnitude and timing of the surgical procedure are as unanswered as those relating to the most appropriate use of the adjuncts themselves. Increasingly, the surgeon and his patient are confronted with a bewildering array of therapeutic options, the long-term outcomes of which are unknown. These relatively rare sarcomas increasingly are distributed among a variety of treatment protocols in which multiple parameters differ. This trend necessitates interinstitutional cooperation if sufficient numbers of patients are to be available for the timely evaluation of treatments in clinical use. Such cooperation and even effective interinstitutional communication are seriously hampered by the lack of uniform language, so that meaningful comparison of treatments is currently impossible. Prime factors include the lack of a consistent definition of the surgery performed and a serviceable surgical staging system encompassing bone and soft tissue. Standard terminology will assure that like and unlike treatments are appropriately compared. Although an effective staging system should serve all members of the multidisciplinary team, the biologic behavior of musculoskeletal sarcomas suggests that the most useful staging system will articulate with the surgical procedure.

We introduce a category of (topological) measure spaces in which inductive limitis exist and where the Banach spaces Open image in new window and Open image in new window (1≤p≤+∞) are isometric for arbitrary inductive systems Open image in new window of (topological) measure spaces.

We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity. We show that, when restricting to SU(2)-gauge invariant operators, the familiar grasping and Wilson loop operators are written as composite operators built from the gauge-invariant ``generalized ladder operators'' recently introduced in the $\mathrm{U}(N)$ approach to intertwiners and spin networks. We comment on quantization ambiguities that appear in the definition of the holonomy operator and use these ambiguities as a toy model to test a class of quantization ambiguities which is present in the standard regularization and definition of the Hamiltonian constraint operator in loop quantum gravity.

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the modern probability theory. Results from Kolmogorov [11], Bochner [2], Choksi [6], Metivier [15], Bourbaki [4], Mallory and Sion [12] among others have paved the way of the deep understanding of this problem. All the above results, however, call for some topological concepts, or at least the ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sufficient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given.

This provides an overview of space science and space systems engineering education at Penn State University. Students at the graduate and undergraduate levels participate in an educational program consisting of three interdependent components: space systems-related courses, space systems project work, and research. Courses range from Introduction to Space Physics to Spacecraft Design. Student project involvement is realized through a number of student-driven space systems projects completed throughout the past two decades. Students are provided opportunities to do independent study projects, honors theses, M.S. theses, and Ph.D. theses on a number of space science and space systems-related topics. Our educational goal is to prepare students at the undergraduate and graduate levels for productive careers in technical and nontechnical fields relating to space systems. Due to student interest, we are developing a certificate in Space Systems Engineering for undergraduates in the College of Engineering. Strengthening Penn State's position in space engineering are its Center for Space Research Programs, membership in the USAF's Space Education Consortium, and its role in serving as the lead institution within the Commonwealth for the Pennsylvania Space Grant Consortium

Parks College of Engineering and Aviation of Saint Louis University [1i] has a tradition of offering an outstanding aerospace engineering education to prepare students at the undergraduate and graduate level for careers in commercial aviation, defense systems, and space systems fields. Courses are offered across the engineering spectrum (aerospace, electrical and computer engineering, and physics departments) ranging from an introduction to aerospace engineering to spacecraft design, spacecraft communications, and space physics. Students participate in courses that include orbital mechanics, space dynamics, spacecraft engineering, and space systems. Senior capstone project work is also included. A separate Astronautics Engineering track as well as a Minor in Space Systems Engineering for non-aerospace engineering students is currently being developed. A, number of student-driven space systems projects are in process that involve design, development, and test of small satellites similar to those recently highlighted in the March 2009 Systems article entitled The First one Hundred University-Class Spacecraft 1981 - 2008. Reference [4] identifies student spacecraft launched over the past 27 years.

The paper considers the problem of complex optimization of the parameters of spacecraft and the space system for Earth remote sensing (ERS). The development (modernization) of equipment and technologies in the planned period is taken into account. The problem is formulated in a deterministic setting. The criterion for solving the task is the reduced total costs for the implementation of the ERS space system project during modernization in the planned period. When searching for a rational solution to the problem, its parametric decomposition is used. Variants of spacecraft modifications as part of the system and the program of modernization of the system are formed separately. The vector of variable parameters includes the parameters of the spacecraft modification and the system modernization program, i.e. the number of modifications of this spacecraft and the timing of their creation. The parameters of the ground segment and the base spacecraft are set. The study shows that the most rational approach to solving the problem is to construct a multi-level design research diagram in accordance with the structure of the system. A two-level design research model and a two-level coordinated optimization method are implemented, including a directed adaptation of the top-level design dependencies. The algorithm for solving the problem includes blocks for forming variants of the spacecraft modification, optimizing the modernization program, assessing the target efficiency, and determining the reduced total costs for the implementation of the system modernization program in the planning period. The possibility of increasing the efficiency of future ERS space systems is explored according to the results of solving the model problem. Using the model example, the parameters and the program of modernization of two alternative options for space systems of different altitudes located in sun-synchronous orbits are comprehensively assessed. The estimation of performance indicators of the considered variants of the systems is given. The assessment of technical and economic characteristics obtained on the basis of the model example can be used for a detailed analysis of the efficiency of future ERS space systems in order to predict their development and expand the field of application.

The paper contains a new proof for the sufficiency in Joel H. Shapiro’s recent characterization of inner functions saying that an analytic self-map φ of the open unit disk is an inner function if and only if the essential norm of the composition operator of symbol φ is equal to √ (1 + |φ(0)|)/(1 − |φ(0)|). The main ingredient in the proof is a formula for the essential norm of a composition operator in terms of Aleksandrov measures obtained by Cima and Matheson. The necessity was originally proved by Joel Shapiro in 1987. A short proof of the necessity, by Aleksandrov measure techniques, was obtained by Jonathan E. Shapiro in 1998. For each holomorphic self-map φ : U → U of the open unit disk U, the composition operator Cφ of symbol φ is defined as follows Cφf = f ◦ φ, f ∈ H. In this definition H is the Hilbert Hardy space on U, i.e., the set of all analytic functions on U with square summable Taylor coefficients. It is well known that each such φ induces a bounded composition operator Cφ on H. Recently Joel Shapiro obtained the following characterization of inner functions [7], (that is of self-maps φ whose radial limit function is unimodular almost everywhere on the unit circle T). Theorem 1. The function φ : U → U is inner if and only if (1) ‖Cφ‖e = √ 1 + |φ(0)| 1− |φ(0)| , where ‖Cφ‖e denotes the essential norm of Cφ. The necessity in the previous equivalence was originally proved in [6]. Jonathan Shapiro [5] observed that Aleksandrov measures can be used Received by the editors on May 7, 2003, and in revised form on May 30, 2003. Copyright c ©2005 Rocky Mountain Mathematics Consortium 1723

Let $\varphi,\psi$ be the analytic self-maps of the unit ball ${\mathbb B}$, we characterize the Hilbert-Schmidt differences of two composition operator $C_\varphi$ and $C_\psi$ on weighted Bergman space $A_\alpha^2$, and give some conclusions about the topological structure of $\mathcal{C}(A_\alpha^2)$, the space of all bounded composition operators on $A_\alpha^2$ endowed with operator norm.

In this paper, we will introduce new sequence Hilbertian space and for it we will show boundedness of composition operators.

The problem of presenting database query results has not been investigated sufficiently. This work proposes an approach to identify effective presentations for the results of database queries. This will be done by considering different kinds of information, such as user goals, the characteristics of the data to be presented, and the relationships among them. Our approach is based on the definition of composition operations which, on the basis of elementary presentation types, allow us to obtain designs of complex final presentations. Some effectiveness criteria are considered in order to identify those presentations which best match the user's goals and cognitive abilities. We consider multimedia environments at both the data and presentation level.

We explore a contact point between two distinct approaches to the confinment problem. We show that BLG-ABJM like theories generate gauge propagators with just the complex pole structure prescribed by the Gribov scenario for confinemnt. This structure, known as i-particles in Gribov-Zwanziger theories, effectively allows the definition of composite operators with a positive K\"{a}ll\'{e}n-Lehmann spectral representation for their two-point functions . Then, these operators satisfy the criteria to describe glue-ball condensates. We calculate the (first order) contribution to the two-point function of the gauge invariant condensate in an ABJM environment, showing its interpretation as a physical particle along K\"{a}ll\'{e}n-Lehmann. In the meantime, we argue for the necessity of absorbing Witten's work on holomorphic complex theories in order to settle the physical interpretation of this non-perturbative scenario.

We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the definition of rule composition operations encodes the non-deterministic sequential concurrent application of rules in Double-Pushout (DPO) and Sesqui-Pushout (SqPO) rewriting with application conditions based upon M-adhesive categories. We uncover an intricate interplay between the category-theoretical concepts of conditions on rules and morphisms, the compositionality and compatibility of certain shift and transport constructions for conditions, and thirdly the property of associativity of the composition of rules.