Polynomials defining distinguished varieties
نویسندگان
چکیده
منابع مشابه
Distinguished Varieties
A distinguished variety is a variety that exits the bidisk through the distinguished boundary. We show that Andô’s inequality for commuting matrix contractions can be sharpened to looking at the maximum modulus on a distinguished variety, not the whole bidisk. We show that uniqueness sets for extremal Pick problems on the bidisk always contain a distinguished variety.
متن کاملDistinguished Representations of Non-negative Polynomials
Let g1, . . . , gr ∈ R[x1, . . . , xn] such that the set K = {g1 ≥ 0, . . . , gr ≥ 0} in Rn is compact. We study the problem of representing polynomials f with f |K ≥ 0 in the form f = s0 + s1g1 + · · · + srgr with sums of squares si, with particular emphasis on the case where f has zeros in K. Assuming that the quadratic module of all such sums is archimedean, we establish a local-global condi...
متن کاملNevanlinna-pick Interpolation on Distinguished Varieties in the Bidisk
This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.
متن کاملDefining "disease"--classification must be distinguished from evaluation.
The term "disease" is discussed with reference to the issues raised by Ian Kennedy in his 1980 Reith Lectures on medical ethics and the definition proposed by Campbell, Scadding, and Roberts. Toon suggests a revised set of definitions based on a distinction between "diseasedness", the opposite of health, and the disease categories used in medicine to distinguish conditions needing specific tre...
متن کاملEquations Defining Symmetric Varieties and Affine Grassmannians
Let σ be a simple involution of an algebraic semisimple group G and let H be the subgroup of G of points fixed by σ. If the restricted root system is of type A,C or BC and G is simply connected or if the restricted root system is of type B and G is adjoint, then we describe a standard monomial theory and the equations for the coordinate ring k[G/H ] using the standard monomial theory and the Pl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2010
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-2010-05275-4