. In [2], the author has extended the above result for Bochner integrals of vectorvalued functions in real or complex Hilbert spaces. If (H ; 〈·, ·〉) is a Hilbert space over K (K = C,R) and f ∈ L ([a, b] ;H), this means that f : [a, b] → H is Bochner measurable on [a, b] and ∫ b a ‖f (t)‖ dt is finite, and there exists a constant K ≥ 1 and a vector e ∈ H, ‖e‖ = 1 such that (1.3) ‖f (t)‖ ≤ K Re ...

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As consequence, we calculate the density of states function of the Bo...

For f ∈ S(R), we consider the Bochner-Riesz operator R of index δ > 0 defined by R̂δf(ξ) = (1− |ξ|)+ f̂(ξ). Then we prove the Bochner-Riesz conjecture which states that if δ > max{d|1/p − 1/2| − 1/2, 0} and p > 1 then R is a bounded operator from L(R) into L(R); moreover, if δ(p) = d(1/p − 1/2) − 1/2 and 1 < p < 2d/(d + 1), then Rδ(p) is a bounded operator from L(R) into L(R).

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As consequence, we calculate the density of states function of the Bo...

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As consequence, we calculate the density of states function of the Bo...

A Bochner-Martinelli-Koppelman type integral formula on submanifolds of pseudoconvex domains in C' is derived ; the result gives, in particular, integral formulas on Stein manifolds. The method of integral representations in several complex variables has been proved to be quite efficient in constructing holomorph_ic functions and more general analytic objects (differential forms solving the á-e...

We prove that the diametral diameter two properties are inherited by F-ideals (e.g., M-ideals). On other hand, these lifted from an M-ideal to superspace under strong geometric assumptions. also show all of stable formation corresponding Köthe–Bochner spaces $$L_p$$ -Bochner spaces). Finally, we investigate when projective tensor product Banach has some property.

We establish a version of Bochner Theorem due to S. Boylan for Banach spaces with a basis.