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51.
By a theorem of Loewner, a continuously differentiable real-valued function on a real interval whose difference quotient is a nonnegative kernel is the restriction of a holomorphic function which has nonnegative imaginary part in the upper half-plane and is holomorphic across the interval. An analogous result is obtained when the difference-quotient kernel has a finite number of negative squares.
52.
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54.
This paper develops a method for obtaining linear fractional representations of a givenn×n matrix valued function which is analytic and contractive in either the unit disc or the open upper half plane. The method depends upon the theory of reproducing kernel Hilbert spaces of vector valued functions developed by de Branges. A self-contained account of the relevant aspects of these spaces to this study is included. In addition, the methods alluded to above are used in conjunction with some ideas of Krein, to develop models for simple, closed symmetric [resp. isometric] operators with equal deficiency indices. A number of related issues and applications are also discussed. 相似文献
55.
We study an order boundedness property in Riesz spaces and investigate Riesz spaces and Banach lattices enjoying this property. 相似文献
56.
Ozcan A 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2005,172(2):238-241
A set of necessary conditions for the choice of diffusion gradient vectors to make the linear equations nonsingular for the estimation of the diffusion matrix are given in a coordinate free manner. The conditions assert that the initial step in the design of a DTI experiment with six or more acquisitions must be to select six valid diffusion gradients first and then add new ones. 相似文献
57.
Banach lattices CD
0(K,E) and CD
(K,E) are introduced and lattice-norm properties of these spaces are investigated. We identify the centre and order continuous dual of these spaces. 相似文献
58.
We study the reproducing kernel Hilbert spaces
with kernels of the form
where S(z1,z2) is a Schur function of two variables z
1,z2
. They are analogs of the spaces
with reproducing kernel (1-S(z)S(w)*)/(1-zw*) introduced by de Branges and Rovnyak l. de Branges and J. Rovnyak, Square Summable Power Series Holt, Rinehart and Winston, New York, 1966. We discuss the characterization of
as a subspace of the Hardy space on the bidisk. The spaces
form a proper subset of the class of the so–called sub–Hardy Hilbert spaces of the bidisk. 相似文献
)S(w_1 ,w_2 )^* }}{{(1 - z_1 w_1^* )(1 - z_2 w_2^* )}}$$ " align="middle" vspace="20%" border="0"> |
59.
We study various aspects of Schur analysis in the slice hyperholomorphic setting. We present two sets of results: first, we give new results on the functional calculus for slice hyperholomorphic functions. In particular, we introduce and study some properties of the Riesz projectors. Then we prove a Beurling–Lax type theorem, the so-called structure theorem. A crucial fact which allows to prove our results is the fact that the right spectrum of a quaternionic linear operator and the point S-spectrum coincide. Finally, we study the Krein–Langer factorization for slice hyperholomorphic generalized Schur functions. Both the Beurling–Lax type theorem and the Krein–Langer factorization are far-reaching results which have not been proved in the quaternionic setting using notions of hyperholomorphy other than slice hyperholomorphy. 相似文献
60.