Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

We study the action of standard intertwining operators on H-fixed generalized vectors in the minimal principal series of a reductive symmetric space G/H of Harish-Chandra's class. The main result is that-after an appropriate normalization-this action is unitary for the unitary principal series. This is an extension of previous work under more restrictive hypotheses on G and H. The present resul...

The description of characters of the innnite symmetric group S1 = lim ?! Sn is considered in the paper as an asymptotical combinatorial problem. It is equivalent to the characterization problem of totally positive sequences. We derive the list of characters, rst obtained by E. Thoma in 1964, using appropriate exact formulae for the number of skew Young tableaux. The character space is treated a...

In this article, we develop an arithmetic analogue of Fourier--Jacobi period integrals for a pair unitary groups equal rank. We construct the so-called cycles, which are algebraic cycles on product Shimura varieties and abelian varieties. propose Gan--Gross--Prasad conjecture these is related to central derivatives certain Rankin--Selberg $L$-functions, relative trace formula approach toward co...

Part I. The Unrefined Trace Formula 7 1. The Selberg trace formula for compact quotient 7 2. Algebraic groups and adeles 11 3. Simple examples 15 4. Noncompact quotient and parabolic subgroups 20 5. Roots and weights 24 6. Statement and discussion of a theorem 29 7. Eisenstein series 31 8. On the proof of the theorem 37 9. Qualitative behaviour of J (f) 46 10. The coarse geometric expansion 53 ...