Displaying similar documents to “Topological imbedding of Laplace distributions in Laplace hyperfunctions”

Premium evaluation for different loss distributions using utility theory

Harman Preet Singh Kapoor, Kanchan Jain (2011)

Discussiones Mathematicae Probability and Statistics

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For any insurance contract to be mutually advantageous to the insurer and the insured, premium setting is an important task for an actuary. The maximum premium ( P m a x ) that an insured is willing to pay can be determined using utility theory. The main focus of this paper is to determine P m a x by considering different forms of the utility function. The loss random variable is assumed to follow different Statistical distributions viz Gamma, Beta, Exponential, Pareto, Weibull, Lognormal and Burr....

An extension theorem for separately holomorphic functions with analytic singularities

Marek Jarnicki, Peter Pflug (2003)

Annales Polonici Mathematici

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Let D j k j be a pseudoconvex domain and let A j D j be a locally pluriregular set, j = 1,...,N. Put X : = j = 1 N A × . . . × A j - 1 × D j × A j + 1 × . . . × A N k + . . . + k N . Let U be an open connected neighborhood of X and let M ⊊ U be an analytic subset. Then there exists an analytic subset M̂ of the “envelope of holomorphy” X̂ of X with M̂ ∩ X ⊂ M such that for every function f separately holomorphic on X∖M there exists an f̂ holomorphic on X̂∖M̂ with f ̂ | X M = f . The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001]. ...

Complete pluripolar graphs in N

Nguyen Quang Dieu, Phung Van Manh (2014)

Annales Polonici Mathematici

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Let F be the Cartesian product of N closed sets in ℂ. We prove that there exists a function g which is continuous on F and holomorphic on the interior of F such that Γ g ( F ) : = ( z , g ( z ) ) : z F is complete pluripolar in N + 1 . Using this result, we show that if D is an analytic polyhedron then there exists a bounded holomorphic function g such that Γ g ( D ) is complete pluripolar in N + 1 . These results are high-dimensional analogs of the previous ones due to Edlund [Complete pluripolar curves and graphs, Ann. Polon. Math....

General Dirichlet series, arithmetic convolution equations and Laplace transforms

Helge Glöckner, Lutz G. Lucht, Štefan Porubský (2009)

Studia Mathematica

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In the earlier paper [Proc. Amer. Math. Soc. 135 (2007)], we studied solutions g: ℕ → ℂ to convolution equations of the form a d g d + a d - 1 g ( d - 1 ) + + a g + a = 0 , where a , . . . , a d : are given arithmetic functions associated with Dirichlet series which converge on some right half plane, and also g is required to be such a function. In this article, we extend our previous results to multidimensional general Dirichlet series of the form x X f ( x ) e - s x ( s k ), where X [ 0 , ) k is an additive subsemigroup. If X is discrete and a certain solvability criterion...

Stratified Whitney jets and tempered ultradistributions on the subanalytic site

N. Honda, G. Morando (2011)

Bulletin de la Société Mathématique de France

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In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X . Then, we define stratified ultradistributions of Beurling and Roumieu type on X . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to X . Second,...

Kernel theorems in spaces of generalized functions

Antoine Delcroix (2010)

Banach Center Publications

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In analogy to the classical isomorphism between ((ℝⁿ), ' ( m ) ) and ' ( m + n ) (resp. ( ( ) , ' ( m ) ) and ' ( m + n ) ), we show that a large class of moderate linear mappings acting between the space C ( ) of compactly supported generalized functions and (ℝⁿ) of generalized functions (resp. the space ( ) of Colombeau rapidly decreasing generalized functions and the space τ ( ) of temperate ones) admits generalized integral representations, with kernels belonging to specific regular subspaces of ( m + n ) (resp. τ ( m + n ) ). The main novelty is to use...

Approximation of sets defined by polynomials with holomorphic coefficients

Marcin Bilski (2012)

Annales Polonici Mathematici

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Let X be an analytic set defined by polynomials whose coefficients a , . . . , a s are holomorphic functions. We formulate conditions on sequences a 1 , ν , . . . , a s , ν of holomorphic functions converging locally uniformly to a , . . . , a s , respectively, such that the sequence X ν of sets obtained by replacing a j ’s by a j , ν ’s in the polynomials converges to X.

J -holomorphic discs and real analytic hypersurfaces

William Alexandre, Emmanuel Mazzilli (2014)

Annales de l’institut Fourier

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We give in 6 a real analytic almost complex structure J , a real analytic hypersurface M and a vector v in the Levi null set at 0 of M , such that there is no germ of J -holomorphic disc γ included in M with γ ( 0 ) = 0 and γ x ( 0 ) = v , although the Levi form of M has constant rank. Then for any hypersurface M and any complex structure J , we give sufficient conditions under which there exists such a germ of disc.

Equicontinuity and Convergent Sequences in the Spaces C ' and M

Jan Kisyński (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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Characterizations of equicontinuity and convergent sequences are given for the space C ' ( ) of rapidly decreasing distributions and the space M ( ) of slowly increasing infinitely differentiable functions.

Characterization of surjective convolution operators on Sato's hyperfunctions

Michael Langenbruch (2010)

Banach Center Publications

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Let μ ( d ) ' be an analytic functional and let T μ be the corresponding convolution operator on Sato’s space ( d ) of hyperfunctions. We show that T μ is surjective iff T μ admits an elementary solution in ( d ) iff the Fourier transform μ̂ satisfies Kawai’s slowly decreasing condition (S). We also show that there are 0 μ ( d ) ' such that T μ is not surjective on ( d ) .

A result on extension of C.R. functions

Makhlouf Derridj, John Erik Fornaess (1983)

Annales de l'institut Fourier

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Let Ω an open set in C 4 near z 0 Ω , λ a suitable holomorphic function near z 0 . If we know that we can solve the following problem (see [M. Derridj, Annali. Sci. Norm. Pisa, Série IV, vol. IX (1981)]) : u = λ f , ( f is a ( 0 , 1 ) form, closed in U ( z 0 ) in U ( z 0 ) with supp ( u ) Ω U ( z 0 ) , then we deduce an extension result for C . R . functions on Ω U ( z 0 ) , as holomorphic fonctions in Ω V ( z 0 ) .

Normal forms of analytic perturbations of quasihomogeneous vector fields: Rigidity, invariant analytic sets and exponentially small approximation

Eric Lombardi, Laurent Stolovitch (2010)

Annales scientifiques de l'École Normale Supérieure

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In this article, we study germs of holomorphic vector fields which are “higher order” perturbations of a quasihomogeneous vector field in a neighborhood of the origin of n , fixed point of the vector fields. We define a “Diophantine condition” on the quasihomogeneous initial part S which ensures that if such a perturbation of S is formally conjugate to S then it is also holomorphically conjugate to it. We study the normal form problem relatively to S . We give a condition on S that ensures...

Shilov boundary for holomorphic functions on some classical Banach spaces

María D. Acosta, Mary Lilian Lourenço (2007)

Studia Mathematica

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Let ( B X ) be the Banach space of all bounded and continuous functions on the closed unit ball B X of a complex Banach space X and holomorphic on the open unit ball, with sup norm, and let u ( B X ) be the subspace of ( B X ) of those functions which are uniformly continuous on B X . A subset B B X is a boundary for ( B X ) if f = s u p x B | f ( x ) | for every f ( B X ) . We prove that for X = d(w,1) (the Lorentz sequence space) and X = C₁(H), the trace class operators, there is a minimal closed boundary for ( B X ) . On the other hand, for X = , the Schreier...