Papers by Stevan Pilipović
Zeitschrift für Analysis und ihre Anwendungen, 1989
On the Behaviour of the Distributional Stieltjes Transformation at the Origin S. PILrPovIO Es wir... more On the Behaviour of the Distributional Stieltjes Transformation at the Origin S. PILrPovIO Es wird das Verhalten der Stieltjes-Transformierten soicher Distributionen aus 'Y',' im Ur. sprung 0 uñtersucht, die ein geeignetes quasiasymptotisches Verhalten in 0 besitzen. Diese ieuen Ergebnisse werden mit Hilfe bekannter Rsultate uber das asymptotische Verhalten hei pc erhalten. Ferner wird auch ein Satz vom Tauberschen Typ fiber das Verhalten in 0 hewiesen. -' 14cc.i1e1yeTcn noBeaeHIle TpaI1C4OpMaIMH CTMrlbTbeca Ta1x HCTpH6ylJMf) MB B Haqajie o opjw uaT 0, ROTObl HMeIOT noj xoanuee KBa3IIaCHMnTOm4eC}coe UOBCeHMe B TOH 0+. 3TM JIOBbIC peayJlbTaml noiyaioca C noMou1,IO M3oecTl(blx o6 acilMnToTu'lecKoM rioaejeun B TO'IRe 00. JoHa3bInaeTcn TaloHe OIJHll pe3yJIbTaT TayöepoBa THI1B 0 noBeeH1aH B T0 q He 0. The behaviour of the distributional Stieltjes transformation at the origin 0 is investigated for distributions of Y' having appropriate quasiasymptotic behaviour at 0+. These new results follow by known ones for the asymptotic behaviour at co. A Tauberian-type result for the behaviour at 0 is also obtained.
arXiv (Cornell University), Nov 19, 2008
We analyze the construction of a sequence space Θ, resp. a sequence of sequence spaces, in order ... more We analyze the construction of a sequence space Θ, resp. a sequence of sequence spaces, in order to have {g i } ∞ i=1 as a Θ-frame or Banach frame for a Banach space X, resp. pre-F -frame or F -frame for a Fréchet space X F = ∩ s∈N0 X s , where {X s } s∈N0 is a sequence of Banach spaces.
ISBS - Conference Proceedings Archive, 2000
The purpose of this study is to analyze the behaviour of muscles in an external instantaneous for... more The purpose of this study is to analyze the behaviour of muscles in an external instantaneous force field. A model is presented which provides a qualitative assessment of what occurs when muscles react to a strong strike or a sudden jerk. In the context of the model, it has been noticed that fine muscles reacted to a strike or jerk differently to massive muscles.
Publicationes Mathematicae Debrecen
By using expansions of elements from S + into Laguerre series we investigate the convolution equa... more By using expansions of elements from S + into Laguerre series we investigate the convolution equations in this space. We give examples of series expansions and present a numerical method for solving convolution equations. Also, we consider the convolution equations in LG e .
Publicationes Mathematicae Debrecen
We introduce the notions of semi-Bloch periodic functions and semi-anti-periodic functions. Stepa... more We introduce the notions of semi-Bloch periodic functions and semi-anti-periodic functions. Stepanov semi-Bloch periodic functions and Stepanov semi-anti-periodic functions are considered, as well. We analyze the invariance of introduced classes under actions of convolution products and briefly explain how one can use the obtained results in the qualitative analysis of solutions of abstract inhomogeneous integro-differential equations.
Filomat, 2019
Microlocal measure ? is associated to a two-scale convergent sequence un over Rd with the limit u... more Microlocal measure ? is associated to a two-scale convergent sequence un over Rd with the limit u ? L2(Rd x Td), Td is a torus, to analyze possible strong limit. ? is an operator valued measure absolutely continuous with respect to the product of scalar microlocal defect measure and a measure on the d-dimensional torus. The result is applied to the first order linear PDE with the oscillating coefficients.
Banach Journal of Mathematical Analysis, 2020
We analyze f -frequently hypercyclic, q-frequently hypercyclic (q > 1) and frequently hypercyclic... more We analyze f -frequently hypercyclic, q-frequently hypercyclic (q > 1) and frequently hypercyclic C 0 -semigroups (q = 1) defined on complex sectors, working in the setting of separable infinite-dimensional Fréchet spaces. Some structural results of ours are given for a general class of F -frequently hypercyclic C 0 -semigroups, as well. We investigate generalized frequently hypercyclic translation semigroups and generalized frequently hypercyclic semigroups induced by semiflows on weighted function spaces. Several illustrative examples are presented.
Proceedings of the American Mathematical Society, 1991
We prove the following assertion: Let T,, j € N , be a sequence in A such that 7" * <fr converges... more We prove the following assertion: Let T,, j € N , be a sequence in A such that 7" * <fr converges to 0 in A as ;'-»«, for any 4> 6 3! . Then T' • -► 0 in S? as j -* oo. The following problem was presented by A. Kamiñski: Let Tj be a sequence in jA such that F * r/> converges to 0 in ¿A as y -> oo for any <fr e <A. Does F -► 0 in A' as j-»oo? K. Keller gave a positive answer to this question in [3] by using an original method based on a theorem of Grothendieck. But the assertion follows directly from the equality of the linear hull of <A * AA, \in(SAAAAA?), and of S" proved by J. Voigt [9] and even earlier by H. Petzeltová and P. Vrbová . Note that lin(^" * 2A
Filomat, 2017
In this paper we consider a sequence of functions in Lp(R), 1 ? p < ? and, in the second part,... more In this paper we consider a sequence of functions in Lp(R), 1 ? p < ? and, in the second part, we include a sequence of real analytic functions without real roots. We obtain several results regarding their convergence or the convergence of the sequence of their analytic representations. We, also, give results about the analytic representation of the product of the boundary functions and other additional results.
We present the basic structural properties of convoluted C-cosine functions and semigroups in a B... more We present the basic structural properties of convoluted C-cosine functions and semigroups in a Banach space setting and consider the corresponding abstract Cauchy problems.
We study various classes of distribution semigroups on the spaces of functions F r , r ∈ R distin... more We study various classes of distribution semigroups on the spaces of functions F r , r ∈ R distinguished by their behavior at the origin.
Series on Analysis, Applications and Computation, 2007
Proceedings of the Edinburgh Mathematical Society, 1998
The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity ... more The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity of a family of differential operators whose coefficients depend on a small parameter ε.There are given necessary and sufficient conditions for the hypoellipticity of a family of differential operators with constant coefficients which depend on ε and behave like powers of ε as ε→0. The solutions of such family of equations should also satisfy the power order estimate with respect to ε.
Proceedings of the American Mathematical Society, 1994
We characterize bounded sets in ultradistributions spaces 3^ p , / € [1, co], S'Wp}, and S'W and ... more We characterize bounded sets in ultradistributions spaces 3^ p , / € [1, co], S'Wp}, and S'W and bounded sets and convergent sequences in 3"W and Sl'Wf} via the convolution by corresponding test functions. The structural theorems for 3f 'jj " and 3'j\ ", t E [ 1, oo], are also given.
Journal of Mathematical Analysis and Applications, 1988
theorems for some new classes of random linear functionals and an application of these results in... more theorems for some new classes of random linear functionals and an application of these results in solving stochastic evolution equations are given.
Journal of Mathematical Analysis and Applications, 1987
The inductive limit of spaces exp, d', p E N (Pilipovic, SIAM J. Math. Anal. 17 (1986), 477484) w... more The inductive limit of spaces exp, d', p E N (Pilipovic, SIAM J. Math. Anal. 17 (1986), 477484) whose elements have unique orthonormal series expansions with exponential growth rate of the corresponding coefficients is to be studied in the first part of the paper. Then, we determine some semigroups of operators on this space. This enables us to solve some classes of infinite order partial differential equations.
Journal of the London Mathematical Society, 1993
Wiener Tauberian theorems are proved for integral transforms of Schwartz distributions in which t... more Wiener Tauberian theorems are proved for integral transforms of Schwartz distributions in which the kernel of the transform belongs to a suitable testing function space.
International Journal of Mathematics and Mathematical Sciences, 1986
In this paper we use the notion ofL-quasiasymptotic at infinity of distributions to obtain a fina... more In this paper we use the notion ofL-quasiasymptotic at infinity of distributions to obtain a final value Tauberian theorem for the distributional Stieltjes transformation.
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Papers by Stevan Pilipović