Tracial moment problems on hypercubes
نویسندگان
چکیده
منابع مشابه
The Truncated Tracial Moment Problem
We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a tracial sequence. We prove that such a sequence can be represented with tracial moments of matrices if its corresponding moment matrix is positive semidefini...
متن کاملThe tracial moment problem and trace-optimization of polynomials
The main topic addressed in this paper is trace-optimization of polynomials in noncommuting (nc) variables: given an nc polynomial f , what is the smallest trace f(A) can attain for a tuple of matrices A? A relaxation using semidefinite programming (SDP) based on sums of hermitian squares and commutators is proposed. While this relaxation is not always exact, it gives effectively computable bou...
متن کاملOn the Convergence of Moment Problems
We study the problem of estimating a nonnegative density, given a finite number of moments. Such problems arise in numerous practical applications. As the number of moments increases, the estimates will always converge weak * as measures, but need not converge weakly in L, . This is related to the existence of functions on a compact metric space which are not essentially Riemann integrable (in ...
متن کاملOn the order of indeterminate moment problems
For an indeterminate moment problem we denote the orthonormal polynomials by Pn. We study the relation between the growth of the function P (z) = ( ∑∞ n=0 |Pn(z)|) and summability properties of the sequence (Pn(z)). Under certain assumptions on the recurrence coefficients from the three term recurrence relation zPn(z) = bnPn+1(z) + anPn(z) + bn−1Pn−1(z), we show that the function P is of order ...
متن کاملTo Determinate Moment Problems
It has been proved that algebraic polynomials P are dense in the space Lp(R, dμ), p∈ (0,∞), iff the measure μ is representable as dμ = wp dν with a finite non-negative Borel measure ν and an upper semi-continuous function w : R → R+ : = [0,∞) such that P is a dense subset of the space C0 w : = {f ∈ C(R) : w(x)f(x) → 0 as |x| → ∞} equipped with the seminorm ‖f‖w := supx∈R w(x)|f(x)|. The similar...
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: Operators and Matrices
سال: 2020
ISSN: 1846-3886
DOI: 10.7153/oam-2020-14-63