Bounds for exponentially stable semigroups

Stable Exponentially Harmonic Maps Between Finsler Manifolds

A Class of Exponentially Bounded Distribution Semigroups

54 M.Mijatović, S.Pilipović 0. Introduction One-time integrated and n-times integrated exponentially bounded semigroups (n-t.i.e.b.s., in short), n ∈ N, of operators on a Banach space introduced by Arendt, were developed in [1-2], [13-16], [19], [22], [29-30] and applied to abstract Cauchy problems with operators which do not generate C0-semigroups. More generally, α-times integrated semigroups...

Excess Risk Bounds for Exponentially Concave Losses

The overarching goal of this paper is to derive excess risk bounds for learning from expconcave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, and negative logarithm loss in portfolio management. In batch setting, we obtai...

Hardy Spaces for Semigroups with Gaussian Bounds

Let Tt = e−tL be a semigroup of self-adjoint linear operators acting on L(X,μ), where (X, d, μ) is a space of homogeneous type. We assume that Tt has an integral kernel Tt(x, y) which satisfies the upper and lower Gaussian bounds: C1 μ(B(x, √ t)) exp ( −c1d(x, y)/t ) ≤ Tt(x, y) ≤ C2 μ(B(x, √ t)) exp ( −c2d(x, y)/t ) . By definition, f belongs to H L if ‖f‖H1 L = ‖ supt>0 |Ttf(x)|‖L1(X,μ) < ∞. W...

stable exponentially harmonic maps between finsler manifolds