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Title: On Parseval Frames of Kernel Functions in de Branges Spaces of Entire Vector Valued Functions
We consider the existence and structure properties of Parseval frames of kernel functions in vector valued de Branges spaces. We develop some sufficient conditions for Parseval sequences by identifying the main construction with Naimark dilation of frames. The dilation occurs by embedding the de Branges space of vector valued functions into a dilated de Branges space of vector valued functions. The embedding also maps the kernel functions associated with a frame sequence of the original space into a Riesz basis for the embedding space. We also develop some sufficient conditions for a dilated de Branges space to have the Kramer sampling property.
Shoikhet, D.; Vajiac, E.
Award ID(s):
1830254 1934884
Publication Date:
Journal Name:
New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative
Sponsoring Org:
National Science Foundation
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