The inverse Laplace transform of the product of two modified Bessel functions where n=1, 2, 3,...
F. M. Ragab (1963)
Annales Polonici Mathematici
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F. M. Ragab (1963)
Annales Polonici Mathematici
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F. Dai, Z. Ditzian, Hongwei Huang (2010)
Studia Mathematica
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Suppose Δ̃ is the Laplace-Beltrami operator on the sphere and where ρ ∈ SO(d). Then and are equivalent for 1 < p < ∞. We note that for even m the relation was recently investigated by the second author. The equivalence yields an extension of the results on sharp Jackson inequalities on the sphere. A new strong converse inequality for given in this paper plays a significant role in the proof.
Nicolas Monod, Henrik Densing Petersen (2014)
Annales de l’institut Fourier
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Let be any group containing an infinite elementary amenable subgroup and let . We construct an exhaustion of by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obstacle to -dimension and gives an answer to a question of Gaboriau.
J. Musiałek (1969)
Annales Polonici Mathematici
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A. M. Mantero, A. Zappa (2009)
Bollettino dell'Unione Matematica Italiana
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Let be thick affine building of type the Laplace operators of ; associated with a pair ; is the Poisson transform of a suitable finitely additive measure on the maximal boundary of ; by using only the combinatorial structure of .
Z. Ditzian (2010)
Studia Mathematica
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Recently it was proved for 1 < p < ∞ that , a modulus of smoothness on the unit sphere, and , a K-functional involving the Laplace-Beltrami operator, are equivalent. It will be shown that the range 1 < p < ∞ is optimal; that is, the equivalence does not hold either for p = ∞ or for p = 1.
Karol Dziedziul (2003)
Applicationes Mathematicae
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The properties of shift invariant operators are proved: It is shown that Q has polynomial order r iff r is the rate of convergence of . A weak saturation theorem is given. If f is replaced by in the weak saturation formula the asymptotics of the expression is calculated. Moreover, bootstrap approximation is introduced.
Jan A. Rempała (1985)
Annales Polonici Mathematici
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Małgorzata Michalska, Maria Nowak, Paweł Sobolewski (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We give new characterizations of the analytic Besov spaces on the unit ball of in terms of oscillations and integral means over some Euclidian balls contained in .
Andrew Linshaw (2011)
Journal of the European Mathematical Society
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The vertex algebra with central charge may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer , it was conjectured in the physics literature that should have a minimal strong generating set consisting of elements. Using a free field realization of due to Kac–Radul, together with a deformed version of Weyl’s first and second fundamental theorems of invariant theory for the standard representation...
Said Bouali, Youssef Bouhafsi (2015)
Mathematica Bohemica
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Let denote the algebra of operators on a complex infinite dimensional Hilbert space . For , the generalized derivation and the elementary operator are defined by and for all . In this paper, we exhibit pairs of operators such that the range-kernel orthogonality of holds for the usual operator norm. We generalize some recent results. We also establish some theorems on the orthogonality of the range and the kernel of with respect to the wider class of unitarily invariant...
Marek Jarnicki, Peter Pflug (2006)
Studia Mathematica
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Let X be a Riemann domain over . If X is a domain of holomorphy with respect to a family ℱ ⊂(X), then there exists a pluripolar set such that every slice of X with a∉ P is a region of holomorphy with respect to the family .
Richard Lechner
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We prove an interpolatory estimate linking the directional Haar projection to the Riesz transform in the context of Bochner-Lebesgue spaces , 1 < p < ∞, provided X is a UMD-space. If , the result is the inequality , (1) where the constant C depends only on n, p, the UMD-constant of X and the Rademacher type of . In order to obtain the interpolatory result (1) we analyze stripe operators , λ ≥ 0, which are used as basic building blocks to dominate the directional Haar projection....
Vincent Guedj (2003)
Bulletin de la Société Mathématique de France
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Let be a dominating rational mapping of first algebraic degree . If is a positive closed current of bidegree on with zero Lelong numbers, we show – under a natural dynamical assumption – that the pullbacks converge to the Green current . For some families of mappings, we get finer convergence results which allow us to characterize all -invariant currents.
Marta Kosek (2011)
Banach Center Publications
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A compact set satisfies Łojasiewicz-Siciak condition if it is polynomially convex and there exist constants B,β > 0 such that if dist(z,K) ≤ 1. (LS) Here denotes the pluricomplex Green function of the set K. We cite theorems where this condition is necessary in the assumptions and list known facts about sets satisfying inequality (LS).
Malkhaz Ashordia (2016)
Mathematica Bohemica
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The Cauchy problem for the system of linear generalized ordinary differential equations in the J. Kurzweil sense , with a unique solution is considered. Necessary and sufficient conditions are obtained for a sequence of the Cauchy problems , to have a unique solution for any sufficiently large such that uniformly on . Presented results are analogous to the sufficient conditions due to Z. Opial for linear ordinary differential systems....
Matthew D. Blair, Christopher D. Sogge (2015)
Journal of the European Mathematical Society
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We extend a result of the second author [27, Theorem 1.1] to dimensions which relates the size of -norms of eigenfunctions for to the amount of -mass in shrinking tubes about unit-length geodesics. The proof uses bilinear oscillatory integral estimates of Lee [22] and a variable coefficient variant of an " removal lemma" of Tao and Vargas [35]. We also use Hörmander’s [20] oscillatory integral theorem and the Cartan–Hadamard theorem to show that, under the assumption of nonpositive...
Ferenc Móricz (2002)
Studia Mathematica
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The harmonic Cesàro operator is defined for a function f in for some 1 ≤ p < ∞ by setting for x > 0 and for x < 0; the harmonic Copson operator ℂ* is defined for a function f in by setting for x ≠ 0. The notation indicates that ℂ and ℂ* are adjoint operators in a certain sense. We present rigorous proofs of the following two commuting relations: (i) If for some 1 ≤ p ≤ 2, then a.e., where f̂ denotes the Fourier transform of f. (ii) If for some 1 < p ≤ 2, then...
Boujemaa Agrebaoui, Raja Hattab (2016)
Czechoslovak Mathematical Journal
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The relative cohomology of the contact Lie superalgebra with coefficients in the space of differential operators acting on tensor densities on , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative -cocycle , which is invariant with respect to the conformal subsuperalgebra of . In this work we study the supergroup case. We give an explicit construction of -cocycles...
Thomas Kalmes (2010)
Studia Mathematica
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We show that if Ω is an open subset of ℝ², then the surjectivity of a partial differential operator P(D) on the space of ultradistributions of Beurling type is equivalent to the surjectivity of P(D) on .
K. Orlov (1980)
Matematički Vesnik
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W. M. Zajączkowski (2007)
Applicationes Mathematicae
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We examine the regularity of solutions to the Stokes system in a neighbourhood of the distinguished axis under the assumptions that the initial velocity v₀ and the external force f belong to some weighted Sobolev spaces. It is assumed that the weight is the (-μ )th power of the distance to the axis. Let , , μ ∈ (0,1). We prove an estimate of the velocity in the norm and of the gradient of the pressure in the norm of . We apply the Fourier transform with respect to the variable along...
Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.
Claudia Garetto (2010)
Banach Center Publications
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We provide a deep investigation of the notions of - and -hypoellipticity for partial differential operators with constant Colombeau coefficients. This involves generalized polynomials and fundamental solutions in the dual of a Colombeau algebra. Sufficient conditions and necessary conditions for - and -hypoellipticity are given
Leokadia Białas-Cież (2011)
Banach Center Publications
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Let E be a compact set in the complex plane, be the Green function of the unbounded component of with pole at infinity and where the supremum is taken over all polynomials of degree at most n, and . The paper deals with recent results concerning a connection between the smoothness of (existence, continuity, Hölder or Lipschitz continuity) and the growth of the sequence . Some additional conditions are given for special classes of sets.