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Supremum and Infimum Convolutions
Logarithmic Sobolev inequalities are closely related to another important class of inequalities in terms of the so-called supremum- and...
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The supremum in specific contexts
This chapter aims to provide formulas for the subdifferential of supremum functions in specific contexts. In these scenarios, an additional structure...
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A New Tour on the Subdifferential of the Supremum Function
This chapter is a survey presenting various characterizations of the subdifferential of the pointwise supremum of convex functions, as well as some...
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Supremum of convex functions
In this chapter, we characterize the subdifferential of pointwise suprema of arbitrarily indexed families of convex functions, defined on a separated...
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On Grunsky norm of univalent functions
We establish an intrinsic lower bound for the Grunsky norm of univalent functions in the disk. This bound sheds light on the intrinsic geometric...
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Numerical Radius and Norm Bounds via the Moore-Penrose Inverse
This paper presents some inner product inequalities for Hilbert space operators having closed ranges. The obtained results are applied to obtain new...
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New Tour on the Subdifferential of Supremum via Finite Sums and Suprema
This paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main...
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On the Pre-Schwarzian Norm of Certain Logharmonic Map**s
We connect the pre-Schwarzian norm of logharmonic map**s to the pre-Schwarzian norm of an analytic function and establish some necessary and...
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Improvement of Menshov’s Theorem on Upper Estimate for the Norm of Maximal Operator
We study the problem of estimating the majorant of partial sums of a series with respect to an orthogonal system. D. E. Menshov established that the...
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Refined Kato inequality and applications to norm and numerical radius inequalities
In this paper, we present refinements of Kato’s inequality; then, we employ these refinements to obtain some norm and numerical radius inequalities....
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Bounded Real Lemma for the Anisotropic Norm of Time-invariant Systems with Multiplicative Noises
AbstractWe consider a discrete-time-invariant system with multiplicative noise with implementation in the state space. The exogenous disturbance is...
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Anisotropic Moser–Trudinger Inequality Involving Ln Norm in the Entire Space ℝn
Let F : ℝ n → [0, + ∞) be a convex function of class C 2 (ℝ n {0}) which is even and positively homogeneous of degree 1, and its polar F 0 represents a...
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Subdifferentiability and polyhedrality of the norm
Let X be an infinite dimensional real Banach space. In this paper, motivated by the work of Contreras et al. (J Math Anal Appl 198:227–236, 1996) we...
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A Family of Semi-norms Between the Numerical Radius and the Operator Norm
This paper introduces a new family of non-negative real-valued functions on the algebra of all bounded linear operators on a Hilbert space. These...
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Norm and Essential Norm of Composition Operators Map** into Weighted Banach Spaces of Harmonic Map**s
Let X be a Banach space of harmonic map**s on the unit disk $$\mathbb...
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Isometries of absolutely continuous function spaces with respect to the sum-norm
In this paper we give a complete description of surjective linear isometries between Banach spaces of absolutely continuous functions on arbitrary...
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On separability of the unbounded norm topology
In this paper we continue the investigation of topological properties of the unbounded norm (un-)topology in normed lattices. We characterize...
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Artificial neural networks with uniform norm-based loss functions
We explore the potential for using a nonsmooth loss function based on the max-norm in the training of an artificial neural network without hidden...
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Phase retrieval and norm retrieval in tensor product space
In signal processing and image science, capturing the phase of measurements is often difficult. In such cases, one needs to reconstruct signal/image...