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Journal articles on the topic 'Theorem of Dirichlet'

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1

S. Phillips, Doug, and Peter Zvengrowski. "CONVERGENCE OF DIRICHLET SERIES AND EULER PRODUCTS." Contributions, Section of Natural, Mathematical and Biotechnical Sciences 38, no. 2 (2017): 153. http://dx.doi.org/10.20903/csnmbs.masa.2017.38.2.111.

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The first part of this paper deals with Dirichlet series, and convergence theorems are proved that strengthen the classical convergence theorem as found e.g. in Serre’s “A Course in Arithmetic.” The second part deals with Euler-type products. A convergence theorem is proved giving sufficient conditions for such products to converge in the half-plane having real part greater than 1/2. Numerical evidence is also presented that suggests that the Euler products corresponding to Dirichlet L-functions L(s, χ), where χ is a primitive Dirichlet character, converge in this half-plane.
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2

ZHANG, LILING. "SET OF EXTREMELY DIRICHLET NON-IMPROVABLE POINTS." Fractals 28, no. 02 (2020): 2050034. http://dx.doi.org/10.1142/s0218348x20500346.

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Let [Formula: see text] be the continued fraction expansion of [Formula: see text]. The growth rate of the product of the partial quotients [Formula: see text] is closely connected with the improvability of Dirichlet’s theorem in the sense that the faster [Formula: see text] grows, the less possibility the improvement of Dirichlet’s theorem has. In this paper, we study the size of the points for which [Formula: see text] grows in a given speed. We call the points of this type as extremely Dirichlet non-improvable points.
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3

Demanze, O., and A. Mouze. "Universal approximation theorem for Dirichlet series." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–11. http://dx.doi.org/10.1155/ijmms/2006/37014.

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The paper deals with an extension theorem by Costakis and Vlachou on simultaneous approximation for holomorphic function to the setting of Dirichlet series, which are absolutely convergent in the right half of the complex plane. The derivation operator used in the analytic case is substituted by a weighted backward shift operator in the Dirichlet case. We show the similarities and extensions in comparing both results. Several density results are proved that finally lead to the main theorem on simultaneous approximation.
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4

Genys, Jonas, and Antanas Laurinčikas. "JOINT WEIGHTED LIMIT THEOREMS FOR GENERAL DIRICHLET SERIES." Mathematical Modelling and Analysis 16, no. 1 (2011): 39–51. http://dx.doi.org/10.3846/13926292.2011.559592.

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In the paper,two joint weighted limit theorems in the sense of weak convergence of probability measures on the complex plane for general Dirichlet series are obtained. The first of them gives only the existence of the limit measure, while in the second theorem,under some additional hypothesis on the weight function, the explicit form of the limit measure is presented. Namely, the limit measure coincides with the distribution of some random element related to considered Dirichlet series.
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5

Mazhar. "AN INTEGRABILITY THEOREM FOR DIRICHLET SERIES." Real Analysis Exchange 20, no. 2 (1994): 726. http://dx.doi.org/10.2307/44152553.

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6

Borwein, David. "A Tauberian theorem concerning Dirichlet series." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 3 (1989): 481–84. http://dx.doi.org/10.1017/s0305004100077859.

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7

Borwein, David. "An Inculsion Theorem for Dirichlet Series." Canadian Mathematical Bulletin 32, no. 4 (1989): 479–81. http://dx.doi.org/10.4153/cmb-1989-069-9.

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8

HAMAHATA, Yoshinori. "OKADA'S THEOREM AND MULTIPLE DIRICHLET SERIES." Kyushu Journal of Mathematics 74, no. 2 (2020): 429–39. http://dx.doi.org/10.2206/kyushujm.74.429.

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9

Gaisin, A. M. "A uniqueness theorem for Dirichlet series." Mathematical Notes of the Academy of Sciences of the USSR 50, no. 2 (1991): 807–12. http://dx.doi.org/10.1007/bf01157566.

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10

Kuznetsov, Alexey. "Lagrange Inversion Theorem for Dirichlet series." Journal of Mathematical Analysis and Applications 493, no. 2 (2021): 124575. http://dx.doi.org/10.1016/j.jmaa.2020.124575.

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11

Hedenmalm, Håkan, and Eero Saksman. "Carleson’s convergence theorem for Dirichlet series." Pacific Journal of Mathematics 208, no. 1 (2003): 85–109. http://dx.doi.org/10.2140/pjm.2003.208.85.

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12

Chouchene, Frej, and Iness Haouala. "Dirichlet Theorem for Jacobi-Dunkl Expansions." Numerical Functional Analysis and Optimization 42, no. 1 (2021): 109–21. http://dx.doi.org/10.1080/01630563.2020.1870042.

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13

Sukla, Indulata. "On Dirichlet convolution method." International Journal of Mathematics and Mathematical Sciences 21, no. 3 (1998): 607–11. http://dx.doi.org/10.1155/s0161171298000842.

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14

Henrici, Andreas. "Nekhoroshev Stability for the Dirichlet Toda Lattice." Symmetry 10, no. 10 (2018): 506. http://dx.doi.org/10.3390/sym10100506.

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In this work, we prove a Nekhoroshev-type stability theorem for the Toda lattice with Dirichlet boundary conditions, i.e., with fixed ends. The Toda lattice is a member of the family of Fermi-Pasta-Ulam (FPU) chains, and in view of the unexpected recurrence phenomena numerically observed in these chains, it has been a long-standing research aim to apply the theory of perturbed integrable systems to these chains, in particular to the Toda lattice which has been shown to be a completely integrable system. The Dirichlet Toda lattice can be treated mathematically by using symmetries of the periodi
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15

Nugraheni, Sekar, and Christiana Rini Indrati. "SOLUSI LEMAH MASALAH DIRICHLET PERSAMAAN DIFERENSIAL PARSIAL LINEAR ELIPTIK ORDER DUA." Journal of Fundamental Mathematics and Applications (JFMA) 1, no. 1 (2018): 1. http://dx.doi.org/10.14710/jfma.v1i1.2.

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The weak solution is one of solutions of the partial differential equations, that is generated from derivative of the distribution. In particular, the definition of a weak solution of the Dirichlet problem for second order linear elliptic partial differential equations is constructed by the definition and the characteristics of Sobolev spaces on Lipschitz domain in R^n. By using the Lax Milgram Theorem, Alternative Fredholm Theorem and Maximum Principle Theorem, we derived the sufficient conditions to ensure the uniqueness of the weak solution of Dirichlet problem for second order linear ellip
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16

Chen, Z. Q., and Z. Zhao. "Switched diffusion processes and systems of elliptic equations: a Dirichlet space approach." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 124, no. 4 (1994): 673–701. http://dx.doi.org/10.1017/s0308210500028596.

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The switched diffusion process associated with a weakly coupled system of elliptic equations is studied via a Dirichlet space approach and is applied to prove the existence theorem of the Cauchy initial problem for the system. A representation theorem for the solution of the Dirichlet boundary value problem and a generalised Skorohod decomposition for the reflecting switched diffusion process are obtained.
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17

Diamantis, Nikolaos, and Dorian Goldfeld. "A converse theorem for double Dirichlet series." American Journal of Mathematics 133, no. 4 (2011): 913–38. http://dx.doi.org/10.1353/ajm.2011.0024.

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18

Schoolmann, I. "On Bohr's theorem for general Dirichlet series." Mathematische Nachrichten 293, no. 8 (2020): 1591–612. http://dx.doi.org/10.1002/mana.201800542.

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19

Petsche, Clayton, and Jeffrey D. Vaaler. "A Dirichlet approximation theorem for group actions." Functiones et Approximatio Commentarii Mathematici 60, no. 2 (2019): 263–75. http://dx.doi.org/10.7169/facm/1755.

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20

Kleinbock, Dmitry, and Nick Wadleigh. "An inhomogeneous Dirichlet theorem via shrinking targets." Compositio Mathematica 155, no. 7 (2019): 1402–23. http://dx.doi.org/10.1112/s0010437x1900719x.

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We give an integrability criterion on a real-valued non-increasing function $\unicode[STIX]{x1D713}$ guaranteeing that for almost all (or almost no) pairs $(A,\mathbf{b})$, where $A$ is a real $m\times n$ matrix and $\mathbf{b}\in \mathbb{R}^{m}$, the system $$\begin{eqnarray}\Vert A\mathbf{q}+\mathbf{b}-\mathbf{p}\Vert ^{m}<\unicode[STIX]{x1D713}(T),\quad \Vert \mathbf{q}\Vert ^{n}<T,\end{eqnarray}$$ is solvable in $\mathbf{p}\in \mathbb{Z}^{m}$, $\mathbf{q}\in \mathbb{Z}^{n}$ for all sufficiently large $T$. The proof consists of a reduction to a shrinking target problem on the space of
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21

Calder�n, C., and M. J. Z�rate. "A mean value theorem on Dirichlet series." Boletim da Sociedade Brasileira de Matem�tica 30, no. 1 (1999): 53–59. http://dx.doi.org/10.1007/bf01235674.

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22

Peiffer, K. "On inversion of the lagrange-dirichlet theorem." Journal of Applied Mathematics and Mechanics 55, no. 4 (1991): 436–41. http://dx.doi.org/10.1016/0021-8928(91)90002-c.

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23

Taelman, Lenny. "A Dirichlet unit theorem for Drinfeld modules." Mathematische Annalen 348, no. 4 (2010): 899–907. http://dx.doi.org/10.1007/s00208-010-0506-6.

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24

Gasiński, Leszek, and Nikolaos S. Papageorgiou. "Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities." Abstract and Applied Analysis 2012 (2012): 1–36. http://dx.doi.org/10.1155/2012/492025.

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We consider a parametric semilinear Dirichlet problem with an unbounded and indefinite potential. In the reaction we have the competing effects of a sublinear (concave) term and of a superlinear (convex) term. Using variational methods coupled with suitable truncation techniques, we prove two multiplicity theorems for small values of the parameter. Both theorems produce five nontrivial smooth solutions, and in the second theorem we provide precise sign information for all the solutions.
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25

Alva, Gerard. "SOBRE LA RECÍPROCA DEL TEOREMA DE DIRICHLET-LAGRANGE." Selecciones Matemáticas 3, no. 2 (2016): 1–4. http://dx.doi.org/10.17268/sel.mat.2016.02.01.

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26

Funakura, Takeo. "On Coefficients of Artin L Functions as Dirichlet Series." Canadian Mathematical Bulletin 33, no. 1 (1990): 50–54. http://dx.doi.org/10.4153/cmb-1990-008-1.

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AbstractThe paper is motivated by a result of Ankeny [1] above Dirichlet L functions in 1952. We generalize this from Dirichlet L functions to Artin L functions of relative abelian extensions, by complementing the ingenious proof of Ankeny's theorem given by Iwasaki [4]. Moreover, we characterize Dirichlet L functions in the class of all Artin L functions in terms of coefficients as Dirichlet series.
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27

Nazarova, Kulzina Zh, Batirkhan Kh Turmetov, and Kairat Id Usmanov. "On a nonlocal boundary value problem with an oblique derivative." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 22, no. 1 (2020): 81–93. http://dx.doi.org/10.15507/2079-6900.22.202001.81-93.

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The work studies the solvability of a nonlocal boundary value problem for the Laplace equation. The nonlocal condition is introduced using transformations in the Rn space carried out by some orthogonal matrices. Examples and properties of such matrices are given. To study the main problem, an auxiliary nonlocal Dirichlet-type problem for the Laplace equation is first solved. This problem is reduced to a vector equation whose elements are the solutions of the classical Dirichlet probem. Under certain conditions for the boundary condition coefficients, theorems on uniqueness and existence of a s
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28

Guadie, Maru. "Stability estimates for discrete harmonic functions on product domains." Applicable Analysis and Discrete Mathematics 7, no. 1 (2013): 143–60. http://dx.doi.org/10.2298/aadm121204025g.

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We study the Dirichlet problem for discrete harmonic functions in unbounded product domains on multidimensional lattices. First we prove some versions of the Phragm?n-Lindel?f theorem and use Fourier series to obtain a discrete analog of the three-line theorem for the gradients of harmonic functions in a strip. Then we derive estimates for the discrete harmonic measure and use elementary spectral inequalities to obtain stability estimates for Dirichlet problem in cylinder domains.
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29

Yeats, Karen. "A Multiplicative Analogue of Schur's Tauberian Theorem." Canadian Mathematical Bulletin 46, no. 3 (2003): 473–80. http://dx.doi.org/10.4153/cmb-2003-046-5.

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AbstractA theorem concerning the asymptotic behaviour of partial sums of the coefficients of products of Dirichlet series is proved using properties of regularly varying functions. This theorem is a multiplicative analogue of Schur's Tauberian theorem for power series.
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30

Watson, Neil A. "A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets." Mathematica Bohemica 130, no. 1 (2005): 1–18. http://dx.doi.org/10.21136/mb.2005.134218.

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31

Bloom, Walter R., and Herbert Heyer. "Non-symmetric translation invariant Dirichlet forms on hypergroups." Bulletin of the Australian Mathematical Society 36, no. 1 (1987): 61–72. http://dx.doi.org/10.1017/s0004972700026307.

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In this note translation-invariant Dirichlet forms on a commutative hypergroup are studied. The main theorem gives a characterisation of an invariant Dirichlet form in terms of the negative definite function associated with it. As an illustration constructions of potentials arising from invariant Dirichlet forms are given. The examples of one- and two-dimensional Jacobi hypergroups yield specifications of invariant Dirichlet forms, particularly in the case of Gelfand pairs of compact type.
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32

Pathan, M. A., H. Kumar, and Priyanka Yadav. "Four dimentional joint moments due to Dirichlet density and their applications in summability of quadruple hypergeometric functions." Boletim da Sociedade Paranaense de Matemática 35, no. 1 (2017): 111. http://dx.doi.org/10.5269/bspm.v35i1.21503.

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Using the Exton’s multiple joint moments in four dimensional spaces due to Dirichlet density and a generalization of Bosanquet and Kestelman theorem , we prove some theorems in summability of the series containing quadruple hypergeomtric functions. These theorems generalize some well known generating functions and multiplication theorems involving product of hypergeometric functions of one and more variables. We discuss some other applications and establish several interesting particular cases. Finally, we obtain an approximation formula of the series involving Exton’s quadruple hypergeometric
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33

Yasuoka, Takashi. "The Dirichlet problem at infinity and complex analysis on Hadamard manifolds." Nagoya Mathematical Journal 106 (June 1987): 79–90. http://dx.doi.org/10.1017/s002776300000088x.

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In this paper we shall study hyperbolicity of Hadamard manifolds.In Section 1 we shall define and solve the Dirichlet problem at infinity for Laplacian J, which gives a partial extension of the result of Anderson and Sullivan in Theorem 1 (cf.). In Section 2 we apply the solution of the Dirichlet problem at infinity to a complex analysis on a Kâhler Hadamard manifold whose metric restricted to every geodesic sphere is conformai to that of the standard sphere. It seems that the sphere at infinity of such a manifold admits a CR-structure. In fact we can define a CR-function at infinity on the sp
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34

Daughton, Austin. "A Hecke correspondence theorem for automorphic integrals with infinite log-polynomial sum period functions." International Journal of Number Theory 10, no. 07 (2014): 1857–79. http://dx.doi.org/10.1142/s1793042114500596.

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We generalize the correspondence between Dirichlet series with finitely many poles that satisfy a functional equation and automorphic integrals with log-polynomial sum period functions. In particular, we extend the correspondence to hold for Dirichlet series with finitely many essential singularities. We also study Dirichlet series with infinitely many poles in a vertical strip. For Hecke groups with λ ≥ 2 and some weights, we prove a similar correspondence for these Dirichlet series. For this case, we provide a way to estimate automorphic integrals with infinite log-polynomial periods by auto
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35

Raghunathan, Ravi. "A converse theorem for Dirichlet series with poles." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 327, no. 3 (1998): 231–35. http://dx.doi.org/10.1016/s0764-4442(98)80138-9.

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36

Ageev, A. A. "Sierpinski's Theorem is Deducible from Euler and Dirichlet." American Mathematical Monthly 101, no. 7 (1994): 659–60. http://dx.doi.org/10.1080/00029890.1994.11997007.

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37

Klusch, Dieter. "The Sampling Theorem, DIRICHLET Series and BESSEL Functions." Mathematische Nachrichten 154, no. 1 (1991): 129–39. http://dx.doi.org/10.1002/mana.19911540111.

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38

Ageev, A. A. "Sierpinski's Theorem is Deducible from Euler and Dirichlet." American Mathematical Monthly 101, no. 7 (1994): 659. http://dx.doi.org/10.2307/2974694.

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39

Macaitiene, Renata. "A discrete universality theorem for general Dirichlet series." Analysis 26, no. 3 (2007): 373–81. http://dx.doi.org/10.1524/anly.2007.26.3.373.

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40

Genys, J., and A. Laurinčikas. "A Joint Limit Theorem for General Dirichlet Series." Lithuanian Mathematical Journal 44, no. 1 (2004): 18–35. http://dx.doi.org/10.1023/b:lima.0000019854.08406.73.

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41

Pańkowski, Łukasz. "Hybrid joint universality theorem for Dirichlet L-functions." Acta Arithmetica 141, no. 1 (2010): 59–72. http://dx.doi.org/10.4064/aa141-1-3.

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42

Eldredge, Nathaniel, and Laurent Saloff-Coste. "Widder’s Representation Theorem for Symmetric Local Dirichlet Spaces." Journal of Theoretical Probability 27, no. 4 (2013): 1178–212. http://dx.doi.org/10.1007/s10959-013-0484-1.

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43

Jiarong, Yu. "A theorem of Picard type for Dirichlet series." Wuhan University Journal of Natural Sciences 2, no. 2 (1997): 129–31. http://dx.doi.org/10.1007/bf02827812.

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44

Trent, Tavan T. "A Corona Theorem for Multipliers on Dirichlet Space." Integral Equations and Operator Theory 49, no. 1 (2004): 123–39. http://dx.doi.org/10.1007/s00020-002-1196-6.

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45

Kranakis, Evangelos, and Michel Pocchiola. "Counting problems relating to a theorem of Dirichlet." Computational Geometry 4, no. 6 (1994): 309–25. http://dx.doi.org/10.1016/0925-7721(94)00013-1.

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46

Klusch, Dieter. "The sampling theorem, Dirichlet series and Hankel transforms." Journal of Computational and Applied Mathematics 44, no. 3 (1992): 261–73. http://dx.doi.org/10.1016/0377-0427(92)90001-e.

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47

Hino, Masanori, and Takashi Kumagai. "A trace theorem for Dirichlet forms on fractals." Journal of Functional Analysis 238, no. 2 (2006): 578–611. http://dx.doi.org/10.1016/j.jfa.2006.05.012.

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48

Bahajji-El Idrissi, H., O. El-Fallah, and K. Kellay. "Havin-Mazya type uniqueness theorem for Dirichlet spaces." Bulletin des Sciences Mathématiques 168 (May 2021): 102967. http://dx.doi.org/10.1016/j.bulsci.2021.102967.

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49

Froese, Richard. "Liouville's Theorem in the Radially Symmetric Case." Canadian Mathematical Bulletin 48, no. 3 (2005): 405–8. http://dx.doi.org/10.4153/cmb-2005-037-7.

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AbstractWe present a very short proof of Liouville's theorem for solutions to a non-uniformly elliptic radially symmetric equation. The proof uses the Ricatti equation satisfied by the Dirichlet to Neumann map.
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50

Everest, G. R. "Diophantine approximation and Dirichlet series." Mathematical Proceedings of the Cambridge Philosophical Society 97, no. 2 (1985): 195–210. http://dx.doi.org/10.1017/s0305004100062757.

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1. Given a sequence an of positive integers, one expects to obtain information on the distribution of these numbers by examining the Dirichlet seriesIn this paper we are going to show how such a series arises from Fröhlich's Galoismodule theory and the use the Thue–Siegel–Roth–Schmidt Theorem as one of the tools in the study of its singularities.
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