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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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The Maximal Function of the Devil’s Staircase is Absolutely Continuous
We study the problem of whether the centered Hardy–Littlewood maximal function of a singular function is absolutely continuous. For a parameter
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Implicit Function Theorems for Continuous Map**s and Their Applications
AbstractLocal and nonlocal implicit function theorems are obtained for closed map**s with a parameter from one Asplund space to another. These...
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On the Banach-Mazur distance between continuous function spaces with scattered boundaries
We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their...
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The Visible-Volume Function of a Set of Cameras is Continuous, Piecewise Rational, Locally Lipschitz, and Semi-Algebraic in All Dimensions
The visible-volume function assigns to a configuration of cameras and a flexible environment in a convex room the volume that can be supervised by...
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Refinement of the Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded Variation
AbstractAn estimate for the convergence rate of the Fourier series of a continuous periodic function of bounded variation is refined.
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Continuous Linear Maps
The continuous linear maps, or operators, are those functions that preserve the structure of normed spaces. They are generalizations of matrices....
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Sharper Bounds for Haar Wavelet Coefficients Corresponding to Continuous Real Valued Function Defined on Unit Interval
Haar wavelet is the only wavelet family with an explicit expression among all Daubechies wavelet families. This beneficial capability is exploited...
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Continuous Random Vectors
Having studied discrete random variables, that is, random variables taking their values in a finite or countable set, we now introduce random...
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Standard Continuous Distributions
Chapter 7 : This chapter introduces standard continuous distributions: exponential, normal, gamma and beta....
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The Infinite-Dimensional Standard and Strict Bounded Real Lemmas in Continuous Time: The Storage Function Approach
The bounded real lemma (BRL) is a classical result in systems theory, which provides a linear matrix inequality criterium for dissipativity, via the...
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On Perturbed Isometries Between the Positive Cones of Certain Continuous Function Spaces
Let X , Y be two compact Hausdorff perfectly normal spaces (in particular, compact metrizable spaces), C ( X ) be the real Banach space of all continuous...
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Function Spaces, Theory and Applications
The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert...
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Robust and accurate reconstruction of the time-dependent continuous volatility from option prices
In this paper, we propose a robust and accurate reconstruction algorithm for the time-dependent continuous volatility function using observed option...
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On the graphs of products of continuous functions and fractal dimensions
In this paper, we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions. More precisely, we show...
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The Continuous Representation Property in Utility Theory
A topological space \((X,\tau )\) satisfies the Continuous...
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Robust utility maximization with nonlinear continuous semimartingales
In this paper we study a robust utility maximization problem in continuous time under model uncertainty. The model uncertainty is governed by a...
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Beyond Discrete and Continuous Random Variables
We provide several examples of singular distributions and review the definition and basic properties of the Riemann–Stieltjes integral. By using the...
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Continuous–Time Deterministic Systems
We now consider a deterministic continuous–time optimal control problem (OCP)Optimal control problem (OCP)continuous–time in which the state process...