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Displaying 61 – 80 of 493

Best constants for some operators associated with the Fourier and Hilbert transforms

B. Hollenbeck, N. J. Kalton, I. E. Verbitsky (2003)

Studia Mathematica

We determine the norm in $L^{p} (ℝ ₊)$ , 1 < p < ∞, of the operator $I - ℱ_{s} ℱ_{c}$ , where $ℱ_{c}$ and $ℱ_{s}$ are respectively the cosine and sine Fourier transforms on the positive real axis, and I is the identity operator. This solves a problem posed in 1984 by M. S. Birman [Bir] which originated in scattering theory for unbounded obstacles in the plane. We also obtain the $L^{p}$ -norms of the operators aI + bH, where H is the Hilbert transform (conjugate function operator) on the circle or real line, for arbitrary real a,b. Best...

BMO estimates for biharmonic multiple layer potentials

Jonathan Cohen (1988)

Studia Mathematica

BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.

Joan Mateu, Joan Verdera Melenchón (1988)

Revista Matemática Iberoamericana

The spectral synthesis theorem for Sobolev spaces of Hedberg and Wolff [7] has been applied in combination with duality, to problems of Lq approximation by analytic and harmonic functions. In fact, such applications were one of the main motivations to consider spectral synthesis problems in the Sobolev space setting. In this paper we go the opposite way in the context of the BMO-H1 duality: we prove a BMO approximation theorem by harmonic functions and then we apply the ideas in its proof to produce...

Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups

Ewa Damek, Andrzej Hulanicki (1995)

Colloquium Mathematicae

Boundaries for left-invariant sub-elliptic operators on semidirect products of nilpotent and abelian groups.

A. Hulanicki, Eva Damek (1990)

Journal für die reine und angewandte Mathematik

Boundary Behavior of Subharmonic Functions on the Unit Disk

Žarko Pavićević, Jela Šušić (1998)

Matematički Vesnik

Boundary integral equations of plane elasticity in domains with peaks.

Maz'ya, V.G., Soloviev, A.A. (2001)

Georgian Mathematical Journal

Boundary integral representations of second derivatives in shape optimization

Karsten Eppler (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

For a shape optimization problem second derivatives are investigated, obtained by a special approach for the description of the boundary variation and the use of a potential ansatz for the state. The natural embedding of the problem in a Banach space allows the application of a standard differential calculus in order to get second derivatives by a straight forward "repetition of differentiation". Moreover, by using boundary value characerizations for more regular data, a complete boundary integral...

Boundary limits of Green's potentials along curves

Jang-Mei Wu (1977)

Studia Mathematica

Boundary properties of second-order partial derivatives of the Poisson integral for a half-space $ℝ_{+}^{k + 1}$ $(k > 1)$ .

Topuria, S. (1998)

Georgian Mathematical Journal

Bounded Harmonic Functions and Positive Ricci Curvature.

Harold Donnelly (1986)

Mathematische Zeitschrift

Bounds for capacities in terms of asymmetry.

Tilak Bhattacharya, Allen Weitsman (1996)

Revista Matemática Iberoamericana

Brownian Excursions and Minimal Thinness. Part III: Applications to the Angular Derivative Problem.

Krysztof Burdza (1986)

Mathematische Zeitschrift

Brownian motion and generalized analytic and inner functions

Alain Bernard, Eddy A. Campbell, A. M. Davie (1979)

Annales de l'institut Fourier

Let $f$ be a mapping from an open set in $R^{p}$ into $R^{q}$ , with $p > q$ . To say that $f$ preserves Brownian motion, up to a random change of clock, means that $f$ is harmonic and that its tangent linear mapping in proportional to a co-isometry. In the case $p = 2$ , $q = 2$ , such conditions signify that $f$ corresponds to an analytic function of one complex variable. We study, essentially that case $p = 3$ , $q = 2$ , in which we prove in particular that such a mapping cannot be “inner” if it is not trivial. A similar result for $p = 4$ , $q = 2$ would solve...

$C^{\infty}$ approximations of convex, subharmonic, and plurisubharmonic functions

R. E. Greene, H. Wu (1979)

Annales scientifiques de l'École Normale Supérieure

Caloric measure on domains bounded by Weierstrass-type graphs.

Bousch, Thierry, Heurteaux, Yanick (2000)

Annales Academiae Scientiarum Fennicae. Mathematica

Capacité analytique et le problème de Painlevé

Hervé Pajot (2003/2004)

Séminaire Bourbaki

Le problème de Painlevé consiste à trouver une caractérisation géométrique des sous-ensembles du plan complexe qui sont effaçables pour les fonctions holomorphes bornées. Ce problème d’analyse complexe a connu ces dernières années des avancées étonnantes, essentiellement grâce au dévelopement de techniques fines d’analyse réelle et de théorie de la mesure géométrique. Dans cet exposé, nous allons présenter et discuter une solution proposée par X. Tolsa en termes de courbure de Menger au problème...

Currently displaying 61 – 80 of 493

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Displaying 61 – 80 of 493

Best constants for some operators associated with the Fourier and Hilbert transforms

BMO estimates for biharmonic multiple layer potentials

BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.

Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups

Boundaries for left-invariant sub-elliptic operators on semidirect products of nilpotent and abelian groups.

Boundary Behavior of Subharmonic Functions on the Unit Disk

Boundary integral equations of plane elasticity in domains with peaks.

Boundary integral representations of second derivatives in shape optimization

Boundary limits of Green's potentials along curves

Boundary properties of second-order partial derivatives of the Poisson integral for a half-space $ℝ_{+}^{k + 1}$ $(k > 1)$ .

Bounded Harmonic Functions and Positive Ricci Curvature.

Bounds for capacities in terms of asymmetry.

Brownian Excursions and Minimal Thinness. Part III: Applications to the Angular Derivative Problem.

Brownian motion and generalized analytic and inner functions

$C^{\infty}$ approximations of convex, subharmonic, and plurisubharmonic functions

Caloric measure on domains bounded by Weierstrass-type graphs.

Capacité analytique et le problème de Painlevé

Certain meromorphic harmonic functions.

Certain subclasses of the class of typically real functions

Choquetova teorie a Dirichletova úloha

Currently displaying 61 – 80 of 493