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Orthogonal Frames in Krein Spaces

MATHEMATICS (2022)

Continuous frames in Krein spaces

Elmar Wagner et al.

Summary: This paper proposes a definition of continuous frames of rank n for Krein spaces and studies their basic properties. Similar to the Hilbert space case, continuous frames are characterized by the analysis, pre-frame, and frame operator, leading to a frame decomposition theorem. The paper discusses the importance of similar, dual, and Parseval frames, as well as reproducing kernels. Additionally, it clarifies the significance of the fundamental symmetry in the formula for the frame operator in a Krein space. As prime examples, it demonstrates how to transfer continuous frames for Hilbert spaces to Krein spaces.

BANACH JOURNAL OF MATHEMATICAL ANALYSIS (2022)

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Soft Frames in Soft Hilbert Spaces

Osmin Ferrer et al.

Summary: This paper introduces the concept of discrete frames on soft Hilbert spaces using soft linear operators, extending the classical notion of frames on Hilbert spaces to algebraic structures on soft sets. The results demonstrate properties of frame operators and prove the frame decomposition theorem for every element in a soft Hilbert space. This theoretical framework has potential applications in signal processing, specifically in modeling data packets for communication networks.

MATHEMATICS (2021)

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Article Mathematics