The Journal of Maternal-Fetal & Neonatal Medicine, 2016
Maternal obesity affects one in every five women giving birth worldwide. This condition is associ... more Maternal obesity affects one in every five women giving birth worldwide. This condition is associated with adverse perinatal outcomes, as well as increased morbidity and mortality for mother and offspring. We carried out a prospective study at the University of Pecs Medical Center, Pecs, Hungary, between 1 January 2013 and 1 January 2014. We enrolled 60 obese (body mass index > 30 kg/m(2)) low-risk pregnant women and 108 age-, ethnicity- and parity-matched non-obese pregnant control subjects. The ST segment of the fetal electrocardiogram was assessed by STAN(®) monitoring. Neonatal outcomes and cord gas analysis of the umbilical vessels were evaluated after birth. No infant with definitive metabolic acidosis was delivered in either group. We observed 32 and 106 ST events in the obese and control group, respectively, but this difference was not statistically significant. To date, none of the infants delivered as part of this study has demonstrated developmental insufficiency. Obesity might not influence the fetal electrocardiogram during labor as an independent risk factor for adverse pregnancy outcomes. Studies with larger cohort sizes are needed to confirm our findings.
Given T 1 ,. .. , Tn commuting power-bounded operators on a Banach space we study under which con... more Given T 1 ,. .. , Tn commuting power-bounded operators on a Banach space we study under which conditions the equality ker(T 1 − I) • • • (Tn − I) = ker(T 1 − I) + • • • + ker(Tn − I) holds true. This problem, known as the periodic decomposition problem, goes back to I. Z. Ruzsa. In this short note we consider the case when T j = T (t j), t j > 0, j = 1,. .. , n for some one-parameter semigroup (T (t)) t≥0. We also look at a generalization of the periodic decomposition problem when instead of the cyclic semigroups {T n j : n ∈ N} more general semigroups of bounded linear operators are considered.
International Journal of Dynamical Systems and Differential Equations, 2007
In this article we survey results concerning asymptotic properties of C0-semigroups on Banach spa... more In this article we survey results concerning asymptotic properties of C0-semigroups on Banach spaces with respect to the weak operator topology. The property "no eigenvalues of the generator on the imaginary axis" is equivalent to weak stability for most time values; a phenomenon called "almost weak stability". Further, sufficient conditions implying the actual weak stability of a C0-semigroup are also given. The individual stability versions are considered as well, using both boundedness of the local resolvent and integrability conditions for the resolvent operator. By a number of examples we explain weak and almost weak stability and illustrate the fundamental difference between them. Where adequate, connections to strong stability are observed, while many historical and bibliographical remarks position the material in the literature. We conclude the paper with some open questions and comments. The fourth author has been supported by the Marie Curie Host Fellowship "Spectral theory for evolution equations", contract number HPMT-CT-2001-00315. 2000 Mathematics Subject Classification. 47D06, 37A25.
A result of Huang and van Neerven [11] establishes weak individual stability for orbits of C0-sem... more A result of Huang and van Neerven [11] establishes weak individual stability for orbits of C0-semigroups under boundedness assumptions on the local resolvent of the generator. We present an elementary proof for this using only the inverse Fourier-transform representation of the orbits of the semigroup in terms of the local resolvent.
Coupled systems of linear differential equations in Banach spaces can be often handled by the the... more Coupled systems of linear differential equations in Banach spaces can be often handled by the theory of C0-semigroups of operator matrices. We study the stability of Lie-Trotter products of such matrix semigroups, and present three classes of examples (abstract delay equations, abstract inhomogeneous equations, abstract dynamic boundary value problems) and some open problems. This survey is based on the papers [1], [2] and [5], to which we refer the interested reader for more details and extensive bibliographical information.
We investigate Lie-Trotter product formulae for abstract nonlinear evolution equations with delay... more We investigate Lie-Trotter product formulae for abstract nonlinear evolution equations with delay. Using results from the theory of nonlinear contraction semigroups in Hilbert spaces, we explain the convergence of the splitting procedure. The order of convergence is also investigated in detail, and some numerical illustrations are presented.
In this paper we further develop the abstract theory of bi-continuous semigroups by combining per... more In this paper we further develop the abstract theory of bi-continuous semigroups by combining perturbation and approximation techniques. The results are then applied to show the positivity for a class of perturbed Ornstein-Uhlenbeck semigroups on the Banach lattice C b (H) of bounded continuous functions on a separable Hilbert space H .
We prove an unbounded perturbation theorem for bi-continuous semigroups on the space of bounded, ... more We prove an unbounded perturbation theorem for bi-continuous semigroups on the space of bounded, continuous functions on the Hilbert space H. This is applied to the Ornstein-Uhlenbeck semigroup, thus providing a purely functional analytic approach to the existence of transition semigroups on C b (H) with bounded non-linear drift.
Proceedings of the American Mathematical Society, 2007
Consider a 1 ,. .. , an ∈ R arbitrary elements. We characterize those functions f : R → R that de... more Consider a 1 ,. .. , an ∈ R arbitrary elements. We characterize those functions f : R → R that decompose into the sum of a j-periodic functions, i.e., f = f 1 +• • •+fn with ∆a j f (x) := f (x+a j)−f (x) = 0. We show that f has such a decomposition if and only if for all partitions B 1 ∪B 2 ∪• • •∪B N = {a 1 ,. .. , an} with B j consisting of commensurable elements with least common multiples b j one has ∆ b 1. .. ∆ b N f = 0. Actually, we prove a more general result for periodic decompositions of functions f : A → R defined on an Abelian group A, in fact, we even consider invariant decompositions of functions f : A → R with respect to commuting, invertible self-mappings of some abstract set A. We also extend our results to functions between torsion free Abelian groups. As a corollary we also obtain that on a torsion free Abelian group the existence of a real valued periodic decomposition of an integer valued function implies the existence of an integer valued periodic decomposition with the same periods.
For a nonempty compact set Ω ⊆ R we determine the maximal possible dimension of a subspace X ⊆ Pm... more For a nonempty compact set Ω ⊆ R we determine the maximal possible dimension of a subspace X ⊆ Pm(Ω) of polynomial functions over Ω with degree at most m which possesses a positive basis. The exact value of this maximum depends on topological features of Ω, and we will see that in many of the cases m can be achieved. Whereas only for low m or finite sets Ω is it possible that we have a subspace X with positive basis and with dim X = m + 1. Hence there is no Ω for which a positive basis exists in Pm for all m ∈ N. k 1 2 [(1 + x) + (1 − x)] n−k , which, when expanded, yields a desired representation in terms of e nk. From this the assertion follows.
We analyze relations between various forms of energies (reciprocal capacities), the transfinite d... more We analyze relations between various forms of energies (reciprocal capacities), the transfinite diameter, various Chebyshev constants and the so-called rendezvous or average number. The latter is originally defined for compact connected metric spaces (X, d) as the (in this case unique) nonnegative real number r with the property that for arbitrary finite point systems {x 1 ,. .. , x n } ⊂ X, there exists some point x ∈ X with the average of the distances d(x, x j) being exactly r. Existence of such a miraculous number has fascinated many people; its normalized version was even named "the magic number" of the metric space. Exploring related notions of general potential theory, as set up, e.g., in the fundamental works of Fuglede and Ohtsuka, we present an alternative, potential theoretic approach to rendezvous numbers.
Journal of Mathematical Analysis and Applications, 2006
We prove a perturbation result for the Ornstein-Uhlenbeck generator on the Hölder space C θ b,loc... more We prove a perturbation result for the Ornstein-Uhlenbeck generator on the Hölder space C θ b,loc (H), H is a separable Hilbert space. As a consequence we obtain the existence of transition semigroups and the solution of elliptic problems associated to stochastic differential equations with non-linear drifts.
ABSTRACT This paper deals with perturbations of the Ornstein–Uhlenbeck operator on L2-spaces with... more ABSTRACT This paper deals with perturbations of the Ornstein–Uhlenbeck operator on L2-spaces with respect to a Gaussian measure μ. We perturb the generator of the Ornstein–Uhlenbeck semigroup by a certain unbounded, non-linear drift, and show various properties of the perturbed semigroup such as compactness and positivity. Strong Feller property, existence and uniqueness of an invariant measure are discussed as well.
We provide a general product formula for the solution of nonautonomous abstract delay equations. ... more We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the theoretical results are demonstrated by some typical numerical examples.
The Journal of Maternal-Fetal & Neonatal Medicine, 2016
Maternal obesity affects one in every five women giving birth worldwide. This condition is associ... more Maternal obesity affects one in every five women giving birth worldwide. This condition is associated with adverse perinatal outcomes, as well as increased morbidity and mortality for mother and offspring. We carried out a prospective study at the University of Pecs Medical Center, Pecs, Hungary, between 1 January 2013 and 1 January 2014. We enrolled 60 obese (body mass index > 30 kg/m(2)) low-risk pregnant women and 108 age-, ethnicity- and parity-matched non-obese pregnant control subjects. The ST segment of the fetal electrocardiogram was assessed by STAN(®) monitoring. Neonatal outcomes and cord gas analysis of the umbilical vessels were evaluated after birth. No infant with definitive metabolic acidosis was delivered in either group. We observed 32 and 106 ST events in the obese and control group, respectively, but this difference was not statistically significant. To date, none of the infants delivered as part of this study has demonstrated developmental insufficiency. Obesity might not influence the fetal electrocardiogram during labor as an independent risk factor for adverse pregnancy outcomes. Studies with larger cohort sizes are needed to confirm our findings.
Given T 1 ,. .. , Tn commuting power-bounded operators on a Banach space we study under which con... more Given T 1 ,. .. , Tn commuting power-bounded operators on a Banach space we study under which conditions the equality ker(T 1 − I) • • • (Tn − I) = ker(T 1 − I) + • • • + ker(Tn − I) holds true. This problem, known as the periodic decomposition problem, goes back to I. Z. Ruzsa. In this short note we consider the case when T j = T (t j), t j > 0, j = 1,. .. , n for some one-parameter semigroup (T (t)) t≥0. We also look at a generalization of the periodic decomposition problem when instead of the cyclic semigroups {T n j : n ∈ N} more general semigroups of bounded linear operators are considered.
International Journal of Dynamical Systems and Differential Equations, 2007
In this article we survey results concerning asymptotic properties of C0-semigroups on Banach spa... more In this article we survey results concerning asymptotic properties of C0-semigroups on Banach spaces with respect to the weak operator topology. The property "no eigenvalues of the generator on the imaginary axis" is equivalent to weak stability for most time values; a phenomenon called "almost weak stability". Further, sufficient conditions implying the actual weak stability of a C0-semigroup are also given. The individual stability versions are considered as well, using both boundedness of the local resolvent and integrability conditions for the resolvent operator. By a number of examples we explain weak and almost weak stability and illustrate the fundamental difference between them. Where adequate, connections to strong stability are observed, while many historical and bibliographical remarks position the material in the literature. We conclude the paper with some open questions and comments. The fourth author has been supported by the Marie Curie Host Fellowship "Spectral theory for evolution equations", contract number HPMT-CT-2001-00315. 2000 Mathematics Subject Classification. 47D06, 37A25.
A result of Huang and van Neerven [11] establishes weak individual stability for orbits of C0-sem... more A result of Huang and van Neerven [11] establishes weak individual stability for orbits of C0-semigroups under boundedness assumptions on the local resolvent of the generator. We present an elementary proof for this using only the inverse Fourier-transform representation of the orbits of the semigroup in terms of the local resolvent.
Coupled systems of linear differential equations in Banach spaces can be often handled by the the... more Coupled systems of linear differential equations in Banach spaces can be often handled by the theory of C0-semigroups of operator matrices. We study the stability of Lie-Trotter products of such matrix semigroups, and present three classes of examples (abstract delay equations, abstract inhomogeneous equations, abstract dynamic boundary value problems) and some open problems. This survey is based on the papers [1], [2] and [5], to which we refer the interested reader for more details and extensive bibliographical information.
We investigate Lie-Trotter product formulae for abstract nonlinear evolution equations with delay... more We investigate Lie-Trotter product formulae for abstract nonlinear evolution equations with delay. Using results from the theory of nonlinear contraction semigroups in Hilbert spaces, we explain the convergence of the splitting procedure. The order of convergence is also investigated in detail, and some numerical illustrations are presented.
In this paper we further develop the abstract theory of bi-continuous semigroups by combining per... more In this paper we further develop the abstract theory of bi-continuous semigroups by combining perturbation and approximation techniques. The results are then applied to show the positivity for a class of perturbed Ornstein-Uhlenbeck semigroups on the Banach lattice C b (H) of bounded continuous functions on a separable Hilbert space H .
We prove an unbounded perturbation theorem for bi-continuous semigroups on the space of bounded, ... more We prove an unbounded perturbation theorem for bi-continuous semigroups on the space of bounded, continuous functions on the Hilbert space H. This is applied to the Ornstein-Uhlenbeck semigroup, thus providing a purely functional analytic approach to the existence of transition semigroups on C b (H) with bounded non-linear drift.
Proceedings of the American Mathematical Society, 2007
Consider a 1 ,. .. , an ∈ R arbitrary elements. We characterize those functions f : R → R that de... more Consider a 1 ,. .. , an ∈ R arbitrary elements. We characterize those functions f : R → R that decompose into the sum of a j-periodic functions, i.e., f = f 1 +• • •+fn with ∆a j f (x) := f (x+a j)−f (x) = 0. We show that f has such a decomposition if and only if for all partitions B 1 ∪B 2 ∪• • •∪B N = {a 1 ,. .. , an} with B j consisting of commensurable elements with least common multiples b j one has ∆ b 1. .. ∆ b N f = 0. Actually, we prove a more general result for periodic decompositions of functions f : A → R defined on an Abelian group A, in fact, we even consider invariant decompositions of functions f : A → R with respect to commuting, invertible self-mappings of some abstract set A. We also extend our results to functions between torsion free Abelian groups. As a corollary we also obtain that on a torsion free Abelian group the existence of a real valued periodic decomposition of an integer valued function implies the existence of an integer valued periodic decomposition with the same periods.
For a nonempty compact set Ω ⊆ R we determine the maximal possible dimension of a subspace X ⊆ Pm... more For a nonempty compact set Ω ⊆ R we determine the maximal possible dimension of a subspace X ⊆ Pm(Ω) of polynomial functions over Ω with degree at most m which possesses a positive basis. The exact value of this maximum depends on topological features of Ω, and we will see that in many of the cases m can be achieved. Whereas only for low m or finite sets Ω is it possible that we have a subspace X with positive basis and with dim X = m + 1. Hence there is no Ω for which a positive basis exists in Pm for all m ∈ N. k 1 2 [(1 + x) + (1 − x)] n−k , which, when expanded, yields a desired representation in terms of e nk. From this the assertion follows.
We analyze relations between various forms of energies (reciprocal capacities), the transfinite d... more We analyze relations between various forms of energies (reciprocal capacities), the transfinite diameter, various Chebyshev constants and the so-called rendezvous or average number. The latter is originally defined for compact connected metric spaces (X, d) as the (in this case unique) nonnegative real number r with the property that for arbitrary finite point systems {x 1 ,. .. , x n } ⊂ X, there exists some point x ∈ X with the average of the distances d(x, x j) being exactly r. Existence of such a miraculous number has fascinated many people; its normalized version was even named "the magic number" of the metric space. Exploring related notions of general potential theory, as set up, e.g., in the fundamental works of Fuglede and Ohtsuka, we present an alternative, potential theoretic approach to rendezvous numbers.
Journal of Mathematical Analysis and Applications, 2006
We prove a perturbation result for the Ornstein-Uhlenbeck generator on the Hölder space C θ b,loc... more We prove a perturbation result for the Ornstein-Uhlenbeck generator on the Hölder space C θ b,loc (H), H is a separable Hilbert space. As a consequence we obtain the existence of transition semigroups and the solution of elliptic problems associated to stochastic differential equations with non-linear drifts.
ABSTRACT This paper deals with perturbations of the Ornstein–Uhlenbeck operator on L2-spaces with... more ABSTRACT This paper deals with perturbations of the Ornstein–Uhlenbeck operator on L2-spaces with respect to a Gaussian measure μ. We perturb the generator of the Ornstein–Uhlenbeck semigroup by a certain unbounded, non-linear drift, and show various properties of the perturbed semigroup such as compactness and positivity. Strong Feller property, existence and uniqueness of an invariant measure are discussed as well.
We provide a general product formula for the solution of nonautonomous abstract delay equations. ... more We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the theoretical results are demonstrated by some typical numerical examples.
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Papers by Balint Farkas