On the Green type kernels on the half space in ${\mathbb {R}}^n$

Masayuki Itô

Displaying similar documents to “On the Green type kernels on the half space in $ℝ^{n}$ ”

Some remarks on the existence of a resolvent

Masanori Kishi (1975)

Annales de l'institut Fourier

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Noting that a resolvent is associated with a convolution kernel $x$ satisfying the domination principle if and only if $x$ has the dominated convergence property, we give 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 product formula on noncompact Grassmannians

Piotr Graczyk, Patrice Sawyer (2013)

Colloquium Mathematicae

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We study the absolute continuity of the convolution $δ_{e^{X}}^{♮} * δ_{e^{Y}}^{♮}$ of two orbital measures on the symmetric space SO₀(p,q)/SO(p)×SO(q), q > p. We prove sharp conditions on X,Y ∈ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions. We show that the sharp criterion developed for SO₀(p,q)/SO(p)×SO(q) also serves for the spaces SU(p,q)/S(U(p)×U(q)) and Sp(p,q)/Sp(p)×Sp(q), q > p. We moreover apply our results to...

A comparison on the commutative neutrix convolution of distributions and the exchange formula

Adem Kiliçman (2001)

Czechoslovak Mathematical Journal

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Let $\tilde{f}$ , $\tilde{g}$ be ultradistributions in $𝒵^{'}$ and let ${\tilde{f}}_{n} = \tilde{f} * δ_{n}$ and ${\tilde{g}}_{n} = \tilde{g} * σ_{n}$ where ${δ_{n}}$ is a sequence in $𝒵$ which converges to the Dirac-delta function $δ$ . Then the neutrix product $\tilde{f} ⋄ \tilde{g}$ is defined on the space of ultradistributions $𝒵^{'}$ as the neutrix limit of the sequence ${\frac{1}{2} ({\tilde{f}}_{n} \tilde{g} + \tilde{f} {\tilde{g}}_{n})}$ provided the limit $\tilde{h}$ exist in the sense that $\underset{n \to \infty}{N - l i m} \frac{1}{2} 〈 {\tilde{f}}_{n} \tilde{g} + \tilde{f} {\tilde{g}}_{n}, ψ 〉 = 〈 \tilde{h}, ψ 〉$ for all $ψ$ in $𝒵$ . We also prove that the neutrix convolution product $f ♦ * g$ exist in $𝒟^{'}$ , if and only if the neutrix product $\tilde{f} ⋄ \tilde{g}$ exist in $𝒵^{'}$ and the exchange formula $F (f ♦ * g) = \tilde{f} ⋄ \tilde{g}$ is then satisfied.

On Deny's characterization of the potential kernel for a convolution Feller semi-group

John C. Taylor (1975)

Annales de l'institut Fourier

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The convolution kernels $V f = f * x$ on a homogeneous space $E = G / K$ , where $K$ is a compact sub-group of $G$ , that satisfy the complete maximum principle are characterized. Deny’s result for abelian groups $G$ , but with a stronger hypothesis, is a special case.

Compact convolution operators between $L_{p} (G)$ -spaces

G. Crombez, W. Govaerts (1978)

Colloquium Mathematicae

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Displaying similar documents to “On the Green type kernels on the half space in ℝ n ”

Some remarks on the existence of a resolvent

On a theorem of M. Itô

On the product formula on noncompact Grassmannians

A comparison on the commutative neutrix convolution of distributions and the exchange formula

On Deny's characterization of the potential kernel for a convolution Feller semi-group

Compact convolution operators between L p ( G ) -spaces

Displaying similar documents to “On the Green type kernels on the half space in $ℝ^{n}$ ”

Compact convolution operators between $L_{p} (G)$ -spaces