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Szego Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds
Let X be an abstract not necessarily compact orientable CR manifold of dimension 2n−1, n⩾2, and let Lk be the k-th tensor power of a CR complex line bundle L over X. Given q∈{0,1,…,n−1}, let □(q)b,k be the Gaffney extension of Kohn Laplacian for (0,q) forms with values in Lk. For λ≥0, let Π(q)k,≤λ:=E((−∞,λ]), where E denotes the spectral measure of □(q)b,k. In this work, the author proves that Π(q)k,≤k−N0F∗k, FkΠ(q)k,≤k−N0F∗k, N0≥1, admit asymptotic expansions with respect to k on the non-degenerate part of the characteristic manifold of □(q)b,k, where Fk is some kind of microlocal cut-off function. Moreover, we show that FkΠ(q)k,≤0F∗k admits a full asymptotic expansion with respect to k if □(q)b,k has small spectral gap property with respect to Fk and Π(q)k,≤0 is k-negligible away the diagonal with respect to Fk. By using these asymptotics, the authors establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR S1 action.
Orthogonal Polynomials on the Unit Circle: Spectral theory
Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.
Szegő's Theorem and Its Descendants
This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.
Orthogonal Polynomials on the Unit Circle
This two-part volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line. The book is suitable for graduate students and researchers interested in analysis.
The New Handbook of Research on Music Teaching and Learning
Featuring chapters by the world's foremost scholars in music education and cognition, this handbook is a convenient collection of current research on music teaching and learning. This comprehensive work includes sections on arts advocacy, music and medicine, teacher education, and studio instruction, among other subjects, making it an essential reference for music education programs. The original Handbook of Research on Music Teaching and Learning, published in 1992 with the sponsorship of the Music Educators National Conference (MENC), was hailed as "a welcome addition to the literature on music education because it serves to provide definition and unity to a broad and complex field" (Choic...
Ethnomusicology
First published in 2011. Routledge is an imprint of Taylor & Francis, an informa company.
Praxial Music Education
Praxial Music Education is a collection of essays by nineteen internationally recognized scholars in music education. Each essay offers critical reflections on a key topic in contemporary music education. The starting point of each essay, and the unifying thread of this collection, is the "praxial" philosophy of music education explained in Elliott's Music Matters: A New Philosophy of Music Education (OUP, 1995). This philosophy argues for a socially and artistically grounded concept of music and music education, challenging the field's traditional "absolutist" foundations. Praxial Music Education is both a critical companion to Music Matters, and an independent text on contemporary issues i...
The Arts Go to School
Discover the power the arts bring to every aspect of learning. Incorporating the arts in your classroom opens up new possibilities, expands the mind, creates a thirst for knowledge, and helps students become more open to the world around them, offering another way of thinking about, being in, and constructing our world. Too often classroom teachers face the challenge of teaching the arts without the background or support they need. The Arts Go to School explores every aspect of implementing and integrating the arts into both the curriculum and everyday life. It contains a wealth of classroom activities that help kids give form to their thoughts and feelings. This easy-to-use resource feature...
Global Pop, Local Language
Cultural Studies -- Ethnomusicology Why would a punk band popular only in Indonesia cut songs in no other language than English? If you're rapping in Tanzania and Malawi, where hip hop has a growing audience, what do you rhyme in? Swahili? Chichewa? English? Some combination of these? Global Pop, Local Language examines how performers and audiences from a wide range of cultures deal with the issue of language choice and dialect in popular music. Related issues confront performers of Latin music in the U.S., drum and bass MCs in Toronto, and rappers, rockers, and traditional folk singers from England and Ireland to France, Germany, Belarus, Nepal, China, New Zealand, Hawaii, and beyond. For p...
