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Displaying 741 – 760 of 3651

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Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.

K. Trimèche (1996)

Collectanea Mathematica

In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.

Control for Schrödinger operators on 2-tori: rough potentials

Jean Bourgain, Nicolas Burq, Maciej Zworski (2013)

Journal of the European Mathematical Society

For the Schrödinger equation, ( i t + ) u = 0 on a torus, an arbitrary non-empty open set Ω provides control and observability of the solution: u t = 0 L 2 ( 𝕋 2 ) K T u L 2 ( [ 0 , T ] × Ω ) . We show that the same result remains true for ( i t + - V ) u = 0 where V L 2 ( 𝕋 2 ) , and 𝕋 2 is a (rational or irrational) torus. That extends the results of [1], and [8] where the observability was proved for V C ( 𝕋 2 ) and conjectured for V L ( 𝕋 2 ) . The higher dimensional generalization remains open for V L ( 𝕋 n ) .

Control Norms for Large Control Times

Sergei Ivanov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A control system of the second order in time with control u = u ( t ) L 2 ( [ 0 , T ] ; U ) is considered. If the system is controllable in a strong sense and uT is the control steering the system to the rest at time T, then the L2–norm of uT decreases as 1 / T while the L 1 ( [ 0 , T ] ; U ) –norm of uT is approximately constant. The proof is based on the moment approach and properties of the relevant exponential family. Results are applied to the wave equation with boundary or distributed controls.

Convergence a.e. of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates

María J. Carro, Elena Prestini (2009)

Studia Mathematica

We prove some extrapolation results for operators bounded on radial L p functions with p ∈ (p₀,p₁) and deduce some endpoint estimates. We apply our results to prove the almost everywhere convergence of the spherical partial Fourier integrals and to obtain estimates on maximal Bochner-Riesz type operators acting on radial functions in several weighted spaces.

Convergence in nonisotropic regions of harmonic functions in n

Carme Cascante, Joaquin Ortega (1999)

Studia Mathematica

We study the boundedness in L p ( n ) of the projections onto spaces of functions with spectrum contained in horizontal strips. We obtain some results concerning convergence along nonisotropic regions of harmonic extensions of functions in L p ( n ) with spectrum included in these horizontal strips.

Currently displaying 741 – 760 of 3651