Displaying similar documents to “Some remarks on the existence of a resolvent”

On a theorem of M. Itô

Gunnar Forst (1978)

Annales de l'institut Fourier

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The note gives a simple proof of a result of M. Itô, stating that the set of divisors of a convolution kernel is a convex cone.

On the Green type kernels on the half space in ℝ n

Masayuki Itô (1978)

Annales de l'institut Fourier

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We characterize the Hunt convolution kernels χ on R n ( n ≥ 2 ) whose the Green type kernels on D = { ( x 1 , ... , x n ) ∈ R n ; x 1 > 0 } , V χ : C K ( D ) ∋ f ( χ * f - χ * χ ‾ ) D , satisfy the domination principle. We write f ‾ ( x 1 , x 2 , ... , x n ) = f ( - x 1 , x 2 , ... , x n ) and ( · ) D the restriction of ( · ) to D . This gives that the question raised by H.L. Jackson is affirmatively solved.

Almost everywhere summability of Laguerre series

Krzysztof Stempak (1991)

Studia Mathematica

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We apply a construction of generalized twisted convolution to investigate almost everywhere summability of expansions with respect to the orthonormal system of functions ℓ n a ( x ) = ( n ! / Γ ( n + a + 1 ) ) 1 / 2 e - x / 2 L n a ( x ) , n = 0,1,2,..., in L 2 ( ℝ + , x a d x ) , a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function f ∈ L p ( x a d x ) , 1 ≤ p ≤ ∞, converge to f a.e. The main tool we use is a Hardy-Littlewood type maximal operator associated with a generalized Euclidean convolution.