Norms of characters and Fourier series on compact Lie groups

We prove new estimates for the p norms of irreducible characters of compact Lie groups. These estimates are applied to give negative results on p mean convergence of Fourier series on compact Lie groups.     

Sharp Fourier type and cotype with respect to compact semisimple Lie groups

Sharp Fourier type and cotype of Lebesgue spaces and Schatten classes with respect to an arbitrary compact semisimple Lie group are investigated. In the process, a local variant of the Hausdorff-Young inequality on such groups is given.

     

Estimates from below for Lebesgue constants of Fourier series on compact Lie groups

In this paper the Lebesque constants (L _R ^K (G))_R>0 of Fourier series on compact Lie groups G corresponding to general one-dimensional groupings on the dual object G^{^} are estimated from below by the associated (abelian) Lebesgue constants (L _R ^K (T))_R>0 on a maximal torus T in G. For spherical groupings this leads to the estimate L _R (G)const.R^(l-1)/2, l=dimT2.     

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f ∈ L ¹(G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.     

Sharp Gårding inequality on compact Lie groups

We establish the sharp Gårding inequality on compact Lie groups. The positivity condition is expressed in the non-commutative phase space in terms of the full matrix symbol, which is defined using the representations of the group. Applications are given to the L² and Sobolev boundedness of pseudo-differential operators.     

Central Fourier analysis for Lorentz spaces on compact Lie groups

We determine the critical indexes for theL ^p,q uniform boundedness of the characters of a compact connected semisimple Lie group. These results show a basic difference between the simple and the semisimple case, a situation which does not appear when dealing withL ^p spaces. We provide applications to the general theory of central functions on compact Lie groups.     

Some new results on absolute Riesz summability of infinite series and Fourier series

In this paper, some known results on the absolute Riesz summability factors of infinite series and Fourier series have been proved under weaker conditions. Some new and known results are also obtained.     

Summability of Fourier series for almost-periodic functions on locally compact Abelian groups

Some results concerning the summability of Fourier series of continuous 2π-periodic functions are generalized for the case of almost-periodic functions defined on locally compact Abelian groups.     

Convergence and summability of Fourier series

In this note we study (C, –) summability, 0<1, of Fourier series and their conjugates in the sense of convergence with respect to the L^P norm, 1p+.Translated from Matematicheskie Zametki, Vol. 19, No. 6, pp. 887–898, June, 1976.     

On the harmonic summability of Fourier series

Proceedings - Mathematical Sciences -     

Spherical resolutions for compact Lie groups

Let G be a compact Lie group and A a G-space. When does there exist a relative G-CW-complex (X,A) with free G-action on X\A, such that X has the homology of a sphere? This paper gives sufficient conditions, which can be used for the construction of homotopy representations.