Some Recent Applications of Bilinear Integration

2009 ◽  
pp. 255-269
Author(s):  
Brian Jefferies
Keyword(s):  
Bilinear Integration

scholarly journals Bilinear Integration in Tensor Products

1998 ◽  
Vol 28 (2) ◽  
pp. 517-545 ◽  
Author(s):  
Brian Jefferies ◽  
Susumu Okada
Keyword(s):  
Tensor Products ◽  
Bilinear Integration

scholarly journals Bilinear integration with positive vector measures

2003 ◽  
Vol 75 (2) ◽  
pp. 279-294 ◽  
Author(s):  
Brian Jefferies ◽  
Paul Rothnie
Keyword(s):  
Banach Lattice ◽  
Vector Measures ◽  
Positive Vector ◽  
Positive Elements ◽  
Bilinear Integration

AbstractThe integration of vector (and operator) valued functions with respect to vector (and operator) valued measures can be simplified by assuming that the measures involved take values in the positive elements of a Banach lattice.

scholarly journals The Bartle Bilinear Integration and Carleman Operators

1999 ◽  
Vol 240 (2) ◽  
pp. 324-339 ◽  
Author(s):  
Francisco J. Freniche ◽  
Juan Carlos Garcı́a-Vázquez
Keyword(s):  
Bilinear Integration

Modified Bilinear Integration Algorithm Based on the Modulated Sine Function

2005 ◽  
Vol 219 (8) ◽  
pp. 609-616 ◽  
Author(s):  
Fu-Hwa Liu ◽  
Cheun-Ming Chen
Keyword(s):  
Discrete Time ◽  
Sampling Period ◽  
Sampled Data ◽  
Discrete Time System ◽  
Integration Algorithm ◽  
Controlled System ◽  
Sample Data ◽  
Z Domain ◽  
Natural Response ◽  
Bilinear Integration

This study presents a novel discretization method for converting an analogue controller into its corresponding counterpart for a discrete-time system. The proposed method is appropriate for the natural response curve and, thus, is more effective for certain digitally redesigned systems. Based on the mapping region of the transformation using the proposed method from the s-domain to the z-domain, a transformation involving a modulated parameter n is used to generate a corresponding stable discrete-time controller for a stable continuous-time controller. As a suitable modulated parameter in the proposed transformation is selected to digitalize an analogue-controlled system, the new sampled-data-controlled system achieves a precise discrete-time response, and can also tolerate a large sampling period for sample-data implementation. A simulated example is used to demonstrate the results.

scholarly journals Joint continuity of injective tensor products of vector measures in Banach lattices

2003 ◽  
Vol 74 (2) ◽  
pp. 185-200 ◽  
Author(s):  
Jun Kawabe
Keyword(s):  
Weak Convergence ◽  
Tensor Product ◽  
Convergence Theorem ◽  
Banach Lattices ◽  
Integration Theory ◽  
Vector Measures ◽  
Joint Continuity ◽  
Positive Vector ◽  
Injective Tensor Product ◽  
Bilinear Integration

AbstractIt is shown that the injective tensor product of positive vector measures in certain Banach lattices is jointly continuous with respect to the weak convergence of vector measures. This result is obtained by a diagonal convergence theorem for injective tensor integrals. Our approach to this problem is based on Bartle's bilinear integration theory.

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