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41.
This is the first of a planned sequence of papers on inverse problems for canonical systems of differential equations. It is devoted largely to foundational material (much of which is of independent interest) on the theory of assorted classes of meromorphic matrix valued functions. Particular attention is paid to the structure of J-inner functions and connections with bitangential interpolation problems and reproducing kernel Hilbert spaces. Some new characterizations of regular, singular and strongly regular J-inner functions in terms of the associated reproducing kernel Hilbert spaces are presented.D. Z. Arov wishes to thank the Weizmann Institute of Science for hospitality and support; H. Dym wishes to thank Renee and Jay Weiss for endowing the chair which supports his research. 相似文献
42.
43.
Johnson AM Moshe O Gamboa AS Langloss BW Limtiaco JF Larive CK Hooley RJ 《Inorganic chemistry》2011,50(19):9430-9442
A series of tetracationic M(2)L(4) palladium-pyridyl complexes with endohedral amine functionality have been synthesized. The complexes were analyzed by NMR techniques (including Diffusion NMR and 2D NOESY), electrospray ionization (ESI) mass spectrometry, and X-ray crystallography. The solid state analysis shows a large change in crystal morphology upon introduction of the endohedral amine groups, caused by deleterious interactions between the amines and the triflate counterions from the coordination process. Combination of different ligands allows analysis of ligand exchange rates via NMR analysis, with half-lives on the order of 3 h, independent of the donor properties of the ligand. Self-sorting behavior is observed, with more electron-rich ligands being favored. The amine-containing and extended complexes are strongly fluorescent, giving quantum yields of up to 83%. 相似文献
44.
Harry Dym Jeremy M. Greene J. William Helton Scott A. McCullough 《Journal d'Analyse Mathématique》2009,108(1):19-59
Every symmetric polynomial p = p(x) = p(x
1,..., x
g
) (with real coefficients) in g noncommuting variables x
1,..., x
g
can be written as a sum and difference of squares of noncommutative polynomials:
$
(SDS) p(x) = \sum\limits_{j = 1}^{\sigma _ + } {f_j^ + (x)^T f_j^ + (x)} - \sum\limits_{\ell = 1}^{\sigma _ - } {f_\ell ^ - (x)^T f_\ell ^ - (x)} ,
$
(SDS) p(x) = \sum\limits_{j = 1}^{\sigma _ + } {f_j^ + (x)^T f_j^ + (x)} - \sum\limits_{\ell = 1}^{\sigma _ - } {f_\ell ^ - (x)^T f_\ell ^ - (x)} ,
相似文献
45.
Harry Dym 《纯数学与应用数学通讯》1994,47(2):207-256
A new proof of a recent theorem of Ellis, Gohberg, and Lay, which identifies the number of roots of a “continuous” matrix orthogonal polynomial in the open upper halfplane with the number of negative eigenvalues of a related integral operator is presented. A related extension problem is then formulated and solved in assorted classes of functions which are analytic in the open upper half plane, apart from a finite number of poles. A discrete analogue of this extension problem is also formulated and solved. © 1994 John Wiley & Sons, Inc. 相似文献
46.
H. Dym 《Israel Journal of Mathematics》1974,18(4):391-398
It is proved that ifj is an inner function and ρ(T)=sup|∫(eiγT/j(γ))f(γ)dγ| overf in the unit ball ofH
1, then eitherρ ≡ 1 for allT≧0, or elseρ(T) ↓ 0 exponentially fast asT ↑ ∞. The inner functionsj corresponding to each alternative are classified. 相似文献
47.
The theory of Hilbert spaces of entire functions is used to deduce the changes in the mass distribution of a string effected by a small change in its spectral function. The formula of Gelfand-Levitan emerges as a special case. 相似文献
48.
This paper continues the study of the bitangential inverse input impedance problem for canonical integral systems that was initiated in [ArD6]. The problem is to recover the system, given an input impedance matrix valued function c() (that belongs to the Carathéodory class of p × p matrix valued functions that are holomorphic and have positive real part in the open upper half plane) and a chain of pairs
of entire inner p × p matrix valued functions (that are identified with the associated pairs of the second kind of the matrizant of the system). Formulas for recovering the underlying canonical integral systems are derived by reproducing kernel Hilbert space methods. A number of examples are presented. Special attention is paid to the case when c() is of Wiener class and also when it is both of Wiener class and rational. 相似文献
49.
Let Rij be a given set of μi× μj matrices for i, j=1,…, n and |i?j| ?m, where 0?m?n?1. Necessary and sufficient conditions are established for the existence and uniqueness of an invertible block matrix =[Fij], i,j=1,…, n, such that Fij=Rij for |i?j|?m, F admits either a left or right block triangular factorization, and (F?1)ij=0 for |i?j|>m. The well-known conditions for an invertible block matrix to admit a block triangular factorization emerge for the particular choice m=n?1. The special case in which the given Rij are positive definite (in an appropriate sense) is explored in detail, and an inequality which corresponds to Burg's maximal entropy inequality in the theory of covariance extension is deduced. The block Toeplitz case is also studied. 相似文献
50.
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