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ESSENTIAL SUPREMUM NORM DIFFERENTIABILITY
, 1985
"... ABSTRACT. The points of Gateaux and Frchet differentiability in L(,X) are obtained, where (,Z,) is a finite measure space and X is a real Banach space. An application of these results is given to the space B(LI(,X) of all bounded linear operators from LI(,i) into X KEY WORDS AND PHRASES. Banach spac ..."
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spaces, measurable functions, essentially bounded functions, vectorval ued functions, essential supremum norm, smooth points.
Essential Supremum And Supremum Of Summable Functions
 Numerical Functional Analysis and Optimization
, 1996
"... Let D ae lR N , 0 ! ¯(D) ! +1 and f : D ! lR is an arbitrary summable function. Then the function F (ff) := R fx2D:f(x)ffg (f(x) \Gamma ff) d¯ (ff 2 lR) is continuous, nonnegative, nonincreasing, convex, and has almost everywhere the derivative F 0 (ff) = \Gamma¯[f ff]. Further on, it hold ..."
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Cited by 9 (5 self)
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, it holds ess supf = supfff 2 lR : F (ff) ? 0g, where ess supf denotes the essential supremum of f . These properties can be used for computing ess sup f . As example, two algorithms are stated. If the function f is dense, or lower semicontinuous, or if \Gammaf is robust, then supf = ess supf
Convergence Speed of an Integral Method for Computing the Essential Supremum
 Developments in Global Optimization,pp.153170
, 1997
"... . We give an equivalence between the tasks of computing the essential supremum of a summable function and of finding a certain zero of a onedimensional convex function. Interpreting the integral method as Newtontype method we show that in the case of objective functions with an essential supremum ..."
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Cited by 6 (3 self)
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. We give an equivalence between the tasks of computing the essential supremum of a summable function and of finding a certain zero of a onedimensional convex function. Interpreting the integral method as Newtontype method we show that in the case of objective functions with an essential supremum
A WEIGHTED WIENER’S LEMMA FOR INTEGRAL OPERATORS WITH SCHURTYPE OR ESSENTIALSUPREMUM KERNEL DECAY CONDITIONS
"... Abstract. In communication theory, one may encounter integral operators whose kernels ’ offdiagonal decay is strictly weaker than exponential. In this paper it is shown that if such an operator is invertible, the kernel of the inverse operator exhibits the same type of decay, extending the Banach ∗ ..."
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Abstract. In communication theory, one may encounter integral operators whose kernels ’ offdiagonal decay is strictly weaker than exponential. In this paper it is shown that if such an operator is invertible, the kernel of the inverse operator exhibits the same type of decay, extending the Banach ∗algebraic techniques of Gröchenig and Leinert in [7] to the setting of integral operators on the space of squareintegrable functions. En route, symmetry of the algebras under consideration is established. 1.
Infimum–supremum
, 2007
"... “garcia de galdeano” garcía de galdeano seminario matemático n. 10 PREPUBLICACIONES del seminario matematico 2007 ..."
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“garcia de galdeano” garcía de galdeano seminario matemático n. 10 PREPUBLICACIONES del seminario matematico 2007
TRANSFER AND A SUPREMUM PRINCIPLE FOR ERNA
"... Abstract. Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis proposed around 1995 by Patrick Suppes and Richard Sommer, who also proved its consistency inside PRA. It is based on an earlier system developed by Rolando Chuaqui and Patrick Suppes ..."
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Cited by 1 (1 self)
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Suppes, of which Michal Rössler and Emil Jeřábek have recently proposed a weakened version. We add a Π1transfer principle to ERNA and prove the consistency of the extended theory inside PRA. In this extension of ERNA a Σ1supremum principle ‘uptoinfinitesimals’, and some wellknown calculus results
EQUIVALENT FORMULAE FOR THE SUPREMUM AND STABILITY OF WEIGHTED PSEUDOINVERSES
"... Abstract. During recent decades, there have been a great number of research articles studying interiorpoint methods for solving problems in mathematical programming and constrained optimization. Stewart and O’Leary obtained an upper bound for scaled pseudoinverses sup ‖(W W ∈P 1 2 X) + W 1 2 ‖2 of ..."
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Cited by 1 (0 self)
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of a matrix X where P is a set of diagonal positive definite matrices. We improved their results to obtain the supremum of scaled pseudoinverses and derived the stability property of scaled pseudoinverses. Forsgren further generalized these results to derive the supremum of weighted pseudoinverses sup
THE ASYMPTOTIC BEHAVIOR OF THE DENSITY OF THE SUPREMUM OF LÉVY PROCESSES
"... Abstract. Let us consider a real Lévy process X whose transition probabilities are absolutely continuous and have bounded densities. Then the law of the past supremum of X before any deterministic time t is absolutely continuous on (0, ∞). We show that its density ft(x) is continuous on (0, ∞) if an ..."
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Abstract. Let us consider a real Lévy process X whose transition probabilities are absolutely continuous and have bounded densities. Then the law of the past supremum of X before any deterministic time t is absolutely continuous on (0, ∞). We show that its density ft(x) is continuous on (0
Results 1  10
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26,185