Let e(x, y, λ) be the spectral function and χλ the unit band spectral projection operator, with respect to the LaplaceBeltrami operator ∆M on a closed Riemannian manifold M . We firstly review the one-term asymptotic formula of e(x, x, λ) as λ → ∞ by Hörmander (1968) and the one of ∂ x ∂ β y e(x, y, λ)|x=y as λ → ∞ in a geodesic normal coordinate chart by the author (2004) and the sharp asympto...

In this paper, we study the problem of learning a matrix W from a set of linear measurements. Our formulation consists in solving an optimization problem which involves regularization with a spectral penalty term. That is, the penalty term is a function of the spectrum of the covariance of W . Instances of this problem in machine learning include multi-task learning, collaborative filtering and...

In this paper, we study the problem of learning a matrix W from a set of linear measurements. Our formulation consists in solving an optimization problem which involves regularization with a spectral penalty term. That is, the penalty term is a function of the spectrum of the covariance of W . Instances of this problem in machine learning include multi-task learning, collaborative filtering and...

‎We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives‎ ‎of global normalizing factors associated to intertwining operators for the following reductive groups over number fields‎: ‎inner forms of $operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$‎. ‎This estimate is a key in...

TELEPHO E-BASED TEXT-DEPE DE T SPEAKER VERIFICATIO In this thesis, we investigate model selection and channel variability issues on telephone-based text-dependent speaker verification applications. Due to the lack of an appropriate database for the task, we collected two multi-channel speaker recognition databases which are referred to as text-dependent variable text (TDVT-D) and textdependent ...

We establish several mathematical and computational properties of the nuclear norm for higher-order tensors. We show that like tensor rank, tensor nuclear norm is dependent on the choice of base field — the value of the nuclear norm of a real 3-tensor depends on whether we regard it as a real 3-tensor or a complex 3-tensor with real entries. We show that every tensor has a nuclear norm attainin...

We introduce the notion of Stieltjes integral with respect to the spectral measure corresponding to a normal operator. Sufficient conditions for the existence of this integral are given, and estimates for its norm are established. The results are applied to operator Sylvester and Riccati equations. Assuming that the spectrum of a closed densely defined operator A does not have common points wit...

in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.