Erratum to “The Partial Inner Product Space Method: A Quick Overview”

The Partial Inner Product Space Method: A Quick Overview

Many families of function spaces play a central role in analysis, in particular, in signal processing e.g., wavelet or Gabor analysis . Typical are L spaces, Besov spaces, amalgam spaces, or modulation spaces. In all these cases, the parameter indexing the family measures the behavior regularity, decay properties of particular functions or operators. It turns out that all these space families a...

A tensor product approach to the abstract partial fourier transforms over semi-direct product groups

In this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to non-Abelian case.

Partial Inner Product Spaces: Some Categorical Aspects

Novel Inner Product Encryption Resistant to Partial Collusion Attacks

Inner product encryption (IPE) is a new cryptographic primitive initially proposed by Abdalla et al. in 2015. IPE can be classified into public-key IPE and secret-key IPE. The currently proposed PK-IPE schemes can-not resist the following collusion attack: an invalid user that holds no private key can ”buy” a combined key generated from multiple collusion adversaries, and the user can use this ...

The Lanczos Method with Semi-inner Product

The spectral transformation Lanczos method is very popular for solving large scale Her-mitian generalized eigenvalue problems. The method uses a special inner product so that the symmetric Lanczos method can be used. Sometimes, a semi-inner product must be used. This may lead to instabilities and breakdown. In this paper, we suggest a cure for breakdown by use of an implicit restart in the Lanc...