According to [9, 8], the initial datum of noncommutative differential geometry is a spectral triple (A,H, D) (see Section 3.1 for the definition), which provides a description of the corresponding geometrical space in terms of spectral data of geometrical operators on this space. The purpose of this paper is to construct spectral triples given by transversally elliptic operators with respect to...

We construct a family of self-adjoint operators DN , N ∈ Z, which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CPq, for any ` ≥ 2 and 0 < q < 1. They provide 0-dimensional equivariant even spectral triples. If ` is odd and N = 1 2 (` + 1), the spectral triple is real with KO-dimension 2` mod 8.

In this paper we propose two algorithms for the restoration of images based on the bispectrum. The bispectrum of a signal is the Fourier transform of its triple correlation. While second-order statistics (e.g., correlation function, power spectrum, etc.) do not provide any information about the phase of the signal, third-order statistics (e.g., triple correlation, bispectrum, etc.) allow the re...

Context. One science goal of the upcoming Planck mission is to perform a full-sky cluster survey based on the Sunyaev-Zel’dovich (SZ) effect, which leads to the question of how such a survey would be affected by cosmological models with a different history of structure formation than ΛCDM. One class of these models are early dark energy (EDE) cosmologies, where the dark energy contribution does...

SCA(Side-channel analysis) is a well-known method to recover the sensitive data stored in security products. Meanwhile numerous countermeasures for hardware implementation of cryptographic algorithms are proposed to protect the internal data against this attack fortunately. However, some designs are not aware that the protection of the plaintext and ciphertext is also crucial. In this work, we ...

In this paper we investigate the index theory of transversally elliptic pseudo-differential operators in the framework of noncommutative geometry. We give examples of spectral triples in the sense of Alain Connes and Henri Moscovici in [12] that are transversally elliptic but nonelliptic. We prove that these spectral triples satisfy the conditions which ensure the Connes-Moscovici local index f...

We show that the algebra A of a commutative unital spectral triple (A,H,D) satisfying several additional conditions, slightly stronger than those proposed by Connes, is the algebra of smooth functions on a compact spin manifold.

We give a new sufficient condition on a spectral triple to ensure that the quantum group of orientation and volume preserving isometries defined in [5] has a C∗-action on the underlying C∗ algebra.