共查询到20条相似文献,搜索用时 0 毫秒
1.
Yuriy M. Dyukarev Bernd Fritzsche Bernd Kirstein Conrad Mädler 《Complex Analysis and Operator Theory》2010,4(4):905-951
We study two slightly different versions of truncated generalized matricial moment problems of Stieltjes type. A central topic is the construction and investigation of distinguished solutions of both moment problems under consideration. These solutions turn out to be nonnegative Hermitian Borel measures on the real axis which are concentrated on a finite number of points. Our approach is mainly algebraic. It is based on the use of particular matrix polynomials constructed from a nonnegative Hermitian block Hankel matrix. 相似文献
2.
Florian-Horia Vasilescu 《Integral Equations and Operator Theory》2014,79(3):301-335
We present a new approach to truncated and full moment problems, via idempotent elements with respect to associated square positive Riesz functionals. The existence of representing measures for such functionals is characterized via some intrinsic conditions. 相似文献
3.
Symmetric VSV decompositions are new rank-revealing decompositions that exploit and preserve symmetry. Truncated VSV solutions are stabilized solutions computed by neglecting blocks in the VSV decomposition with small norm. We compare the truncated VSV solutions with truncated SVD solutions and give perturbation bounds for the VSV solutions. Numerical examples illustrate our results. 相似文献
4.
Raúl E. Curto Lawrence A. Fialkow H. Michael Möller 《Integral Equations and Operator Theory》2008,60(2):177-200
For a degree 2n real d-dimensional multisequence to have a representing measure μ, it is necessary for the associated moment matrix to be positive semidefinite and for the algebraic variety associated to β, , to satisfy rank card as well as the following consistency condition: if a polynomial vanishes on , then . We prove that for the extremal case , positivity of and consistency are sufficient for the existence of a (unique, rank -atomic) representing measure. We also show that in the preceding result, consistency cannot always be replaced by recursiveness
of .
The first-named author’s research was partially supported by NSF Research Grants DMS-0099357 and DMS-0400741. The second-named
author’s research was partially supported by NSF Research Grant DMS-0201430 and DMS-0457138. 相似文献
5.
We study the density problem for a set of polynomials in the space
, where is a measure with finite moments. The approach to this problem is based on methods of the theory of moments, which allows one to formulate sufficient conditions in terms of Nevanlinna functions. 相似文献
6.
Given real numbers
with 00 >0 , the truncated parabolic moment problem for entails finding necessary and sufficient conditions for the existence of a positive Borel measure , supported in the parabola p(x, y) = 0, such that
We prove that admits a representing measure (as above) if and only if the associated moment matrix
is positive semidefinite, recursively generated and has a column relation p(X, Y) = 0, and the algebraic variety () associated to satisfies card
In this case, admits a rank
-atomic (minimal) representing measure.Submitted: August 25, 2003 相似文献
7.
Let Q(x, y) = 0 be an hyperbola in the plane. Given real numbers β ≡ β (2n)={ β ij } i,j ≥ 0,i+j ≤ 2n , with β00 > 0, the truncated Q-hyperbolic moment problem for β entails finding necessary and sufficient conditions for the existence of a positive Borel measure μ, supported in Q(x, y) = 0, such that
We prove that β admits a Q-representing measure μ (as above) if and only if the associated moment matrix
is positive semidefinite, recursively generated, has a column relation Q(X,Y) = 0, and the algebraic variety
associated to β satisfies card
In this case,
if
then β admits a rank
-atomic (minimal) Q-representing measure; if
then β admits a Q-representing measure μ satisfying
相似文献
8.
Lawrence A. Fialkow 《Integral Equations and Operator Theory》2003,45(4):405-435
We solve the truncated complex moment problem for measures supported on the variety K o \mathcal{K}\equiv { z ? \in C: z [(z)\tilde]\widetilde{z} = A+Bz+C [(z)\tilde]\widetilde{z} +Dz 2 ,D 1 \neq 0}. Given a doubly indexed finite sequence of complex numbers g o g(2n):g00,g01,g10,?,g0,2n,g1,2n-1,?,g2n-1,1,g2n,0 \gamma\equiv\gamma^{(2n)}:\gamma_{00},\gamma_{01},\gamma_{10},\ldots,\gamma_{0,2n},\gamma_{1,2n-1},\ldots,\gamma_{2n-1,1},\gamma_{2n,0} , there exists a positive Borel measure m\mu supported in K \mathcal{K} such that gij=ò[`(z)]izj dm (0 £ 1+j £ 2n) \gamma_{ij}=\int\overline{z}^{i}z^{j}\,d\mu\,(0\leq1+j\leq2n) if and only if the moment matrix M(n)( g\gamma ) is positive, recursively generated, with a column dependence relation Z [(Z)\tilde]\widetilde{Z} = A1+BZ +C [(Z)\tilde]\widetilde{Z} +DZ 2, and card V(g) 3\mathcal{V}(\gamma)\geq rank M(n), where V(g)\mathcal{V}(\gamma) is the variety associated to g \gamma . The last condition may be replaced by the condition that there exists a complex number gn,n+1 \gamma_{n,n+1} satisfying gn+1,n o [`(g)]n,n+1=Agn,n-1+Bgn,n+Cgn+1,n-1+Dgn,n+1 \gamma_{n+1,n}\equiv\overline{\gamma}_{n,n+1}=A\gamma_{n,n-1}+B\gamma_{n,n}+C\gamma_{n+1,n-1}+D\gamma_{n,n+1} . We combine these results with a recent theorem of J. Stochel to solve the full complex moment problem for K \mathcal{K} , and we illustrate the connection between the truncated and full moment problems for other varieties as well, including the variety z k = p(z, [(Z)\tilde] \widetilde{Z} ), deg p < k. 相似文献
9.
This paper is concerned with the solution of a certain tangential
Nevanlinna-Pick interpolation for Nevanlinna functions. We use the so-called
block Hankel vector method to establish two intrinsic connections between
the tangential Nevanlinna-Pick interpolation in the Nevanlinna class and the
truncated Hamburger matrix moment problem associated with the block Hankel
vector under consideration: one is a congruent relationship between their
information matrices, and the other is a divisor-remainder connection between
their solutions. These investigations generalize our previous work on
the Nevanlinna-Pick interpolation and power matrix moment problem. 相似文献
10.
Jean-Pierre Gabardo 《Journal of Fourier Analysis and Applications》1994,1(3):249-279
A simple parametrization is given for the set of positive measures with finite support on the circle group T that are solutions
of the truncated trigonometric moment problem:
where the parameters are, up to nonzero multiplicative constants, the polynomials whose roots all have a modulus less than
one. This result is then used to characterize, on a certain natural Hilbert space of polynomials associated with the problem,
all finite "weighted" tight frames of evaluation polynomials. Finally, a new and simple way of parametrizing the whole set
of positive Borel measures on T, solutions of the given
moment problem is deduced, via a limiting argument. 相似文献
11.
12.
13.
E. V. Radkevich 《Journal of Mathematical Sciences》2004,123(5):4428-4455
The paper is devoted to the study of the asymptotic behavior of solutions to linearized systems of equations of the so-called nonequilibrium thermodynamic moments. 相似文献
14.
A moment problem of Hamburger is studied to find a parametric Stieltjes measure from given moments. It is shown that if a deformation, or a dynamics, of moments is governed by a hierarchy of a Kac-van Moerbeke system, then the Stieltjes measure can be constructed explicitly by integrating a hierarchy of Moser's nonlinear dynamical system. The positivity of tau-functions is related to the existence of the Stieltjes measure at a deep level. 相似文献
15.
Charles G. Lange 《Studies in Applied Mathematics》1983,68(3):227-257
A study is made of several nonlinear boundary-value problems of singular perturbation type for which a straightforward application of boundary-layer theory leads to spurious solutions. It is shown that these problems can be treated successfully by a slight modification of the method of matched asymptotic expansions. The analysis leads to several novel features which are not present in routine singular perturbation problems. 相似文献
16.
Partially commutative tensor algebras occur naturally in the algebraic formulation of Wightman field theory. A state on an algebra of this type leads via GNS-construction to a partially commutative family of hermitean operators on Hilbert space. We discuss the question when these operators can be extended to self adjoint operators preserving the commutation properties and state a necessary and sufficient condition for the existence of such an extension in terms of a positivity property of the state. 相似文献
17.
F. Oravecz 《Acta Mathematica Hungarica》2001,92(3):173-177
The sequence of Catalan numbers is known to be the moments of the Wigner law. A characterization of this sequence is given in terms of some determinants and the moment sequence of the q-Gaussian law is characterized in a similar fashion. 相似文献
18.
S. M. Zagorodnyuk 《Ukrainian Mathematical Journal》2010,62(4):537-551
We obtain necessary and sufficient conditions for the solvability of the strong matrix Hamburger moment problem. We describe all solutions of the moment problem by using the fundamental results of A. V. Shtraus on generalized resolvents of symmetric operators. 相似文献
19.
20.
Fritzsche Bernd Kirstein Bernd Lasarow Andreas 《Integral Equations and Operator Theory》2004,48(3):305-330
We derive statements on rank invariance of Schwarz-Pick-Potapov
block matrices of matrix-valued Schur functions. The rank of these block
matrices coincides with the rank of some block matrices built from the corresponding
section matrices of Taylor coefficients. These results are applied to
the discussion of a matrix version of the classical Schur-Nevanlinna algorithm. 相似文献