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1

Hino, Masanori. A trace theorem for Dirichlet forms on fractals. Research Institute for Mathematical Sciences, 2005.

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2

Benedek, Agnes Ilona. Remarks on a theorem of Å. Pleijel and related topics. INMABB-CONICET, Universidad Nacional del Sur, 2005.

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3

1952-, Bump Daniel, and Friedberg Solomon 1958-, eds. Weyl group multiple Dirichlet series: Type A combinatorial theory. Princeton University Press, 2011.

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4

Solomon, Friedberg, Goldfeld Dorian, and SpringerLink (Online service), eds. Multiple Dirichlet Series, L-functions and Automorphic Forms. Birkhäuser Boston, 2012.

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5

1886, Riesz Marcel b., ed. The general theory of Dirichlet's series. Dover Publications, 2005.

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6

R, Uppuluri V. R., Frankowski K, Odeh Robert E, Davenport James M, and Institute of Mathematical Statistics, eds. Dirichlet integrals of type 2 and their applications. American Mathematical Society, 1985.

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7

Gauss-Dirichlet Conference (2005 Göttingen, Germany). Analytic number theory: A tribute to Gauss and Dirichlet : proceedings of the Gauss-Dirichlet Conference, Göttingen, Germany, June 20-24, 2005. Edited by Duke William 1958- and Tschinkel Yuri. American Mathematical Society, Clay Mathematics Institute, 2007.

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8

Dancer, E. N. Weakly nonlinear Dirichlet problems on long or thin domains. American Mathematical Society, 1993.

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9

Ng, Kai Wang. Dirichlet and Related Distributions: Theory, Methods and Applications. Wiley, 2011.

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10

A Dirichlet problem for distributions and specifications for random fields. American Mathematical Society, 1985.

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11

M, Apostol Tom. Modular functions and Dirichlet series in number theory. 2nd ed. Springer-Verlag, 1990.

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12

M, Apostol Tom. Modular Functions and Dirichlet Series in Number Theory. Springer-Verlag, 1989.

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13

Tenenbaum, Gerald. Introduction à la théorie analytique et probabiliste des nombres. 2nd ed. Société Mathématique de France, 1995.

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14

1983-, Spadaro Emanuele Nunzio, ed. Q-valued functions revisited. American Mathematical Society, 2010.

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15

Obobshchennye diffuzionnye potent︠s︡ialy: [v 2 t.]. 2nd ed. Omega Print, 2011.

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16

Pseudo differential operators & Markov processes. Imperial College Press, 2002.

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17

Jacob, Niels. Pseudo-differential operators and Markov processes. Akademie Verlag, 1996.

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18

Ecole d'été de probabilités de Saint-Flour (35th : 2005), ed. Probability and real trees: École d'Été de Probabilités de Saint-Flour XXXV-2005. Springer, 2008.

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19

D-branes. Cambridge University Press, 2003.

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20

D-branes. Cambridge University Press, 2006.

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21

Burgos Gil, José I. (José Ignacio), 1962- editor, ed. Feynman amplitudes, periods, and motives: International research conference on periods and motives : a modern perspective on renormalization : July 2-6, 2012, Institute de Ciencias Matematicas, Madris, Spain. American Mathematical Society, 2015.

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22

The endoscopic classification of representations orthogonal and symplectic groups. American Mathematical Society, 2013.

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23

PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics (2011 Messina, Italy). Fractal geometry and dynamical systems in pure and applied mathematics. Edited by Carfi David 1971-, Lapidus, Michel L. (Michel Laurent), 1956-, Pearse, Erin P. J., 1975-, Van Frankenhuysen Machiel 1967-, and Mandelbrot Benoit B. American Mathematical Society, 2013.

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24

1953-, Campillo Antonio, ed. Zeta functions in algebra and geometry: Second International Workshop on Zeta Functions in Algebra and Geometry, May 3-7, 2010, Universitat de Les Illes Balears, Palma de Mallorca, Spain. American Mathematical Society, 2012.

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25

Edmunds, D. E., and W. D. Evans. Generalized Dirichlet and Neumann Boundary-Value Problems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0006.

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In this chapter, the generalized or weak interpretation of the Dirichlet and Neumann problems for general elliptic expressions is motivated and then the Lax–Milgram Theorem is used to set the problems in the framework of eigenvalue problems for operators acting in Hilbert space. Results on variational inequalities in Chapter IV are applied to establish Stampacchia’s weak maximum principle, and this leads to the notion of capacity.
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26

Mann, Peter. The Stationary Action Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0007.

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This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse problem is described. The chapter then considers the Ostrogradsky equation and discusses the properties of the extrema using the second-order variation to the action. It then discusses the difference between action functions (of Dirichlet boundary conditions) and action functionals of the extremal path. The different types of boundary conditions (Dirichlet vs Neumann) are elucidated. Topics discussed i
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27

Edmunds, D. E., and W. D. Evans. Second-Order Differential Operators on Arbitrary Open Sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0007.

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In this chapter, three different methods are described for obtaining nice operators generated in some L2 space by second-order differential expressions and either Dirichlet or Neumann boundary conditions. The first is based on sesquilinear forms and the determination of m-sectorial operators by Kato’s First Representation Theorem; the second produces an m-accretive realization by a technique due to Kato using his distributional inequality; the third has its roots in the work of Levinson and Titchmarsh and gives operators T that are such that iT is m-accretive. The class of such operators inclu
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28

1964-, Aspinwall Paul, ed. Dirichlet branes and mirror symmetry. American Mathematical Society, 2009.

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29

The general theory of Dirichlet's series. University Press, 1991.

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30

Dirichlet And Related Distributions Theory Methods And Applications. John Wiley & Sons, 2011.

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31

Ng, Kai Wang, Man-Lai Tang, and Guo-Liang Tian. Dirichlet and Related Distributions: Theory, Methods and Applications. Wiley & Sons, Incorporated, John, 2011.

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32

Ng, Kai Wang, Man-Lai Tang, and Guo-Liang Tian. Dirichlet and Related Distributions: Theory, Methods and Applications. Wiley & Sons, Incorporated, John, 2011.

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33

Ng, Kai Wang, Man-Lai Tang, and Guo-Liang Tian. Dirichlet and Related Distributions: Theory, Methods and Applications. Wiley & Sons, Incorporated, John, 2011.

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34

Apostol, Tom M. Modular functions and Dirichlet series in number theory. Springer, 1997.

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35

China) International Conference on Advances in Structural Dynamics (2000 : Hong Kong. Dirichlet Forms and Stochastic Processes: Proceedings of the International Conference Held in Beijing, China, October 25-31, 1993. Walter de Gruyter, 1995.

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36

Zhi-Ming, Ma, Röckner Michael 1956-, Yan J, and International Conference on Dirichlet Forms and Stochastic Processes (1993 : Beijing, China), eds. Dirichlet forms and stochastic processes: Proceedings of the international conference held in Beijing, China, October 25-31, 1993. W. de Gruyter, 1995.

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37

Keating, Jon, and Nina Snaith. Random permutations and related topics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.25.

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This article considers some topics in random permutations and random partitions highlighting analogies with random matrix theory (RMT). An ensemble of random permutations is determined by a probability distribution on Sn, the set of permutations of [n] := {1, 2, . . . , n}. In many ways, the symmetric group Sn is linked to classical matrix groups. Ensembles of random permutations should be given the same treatment as random matrix ensembles, such as the ensembles of classical compact groups and symmetric spaces of compact type with normalized invariant measure. The article first describes the
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38

Vorlesungen über die Theorie der bestimmten Integrale zwischen reellen Grenzen mit vorzüglicher Berücksichtigung der von P. Gustav Lejeune-Dirichlet in Sommer 1858 gehaltenen Vorträge über bestimmte Integrale. B. G. Teubner, 1991.

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39

Jacob, Niels. Pseudo Differential Operators & Markov Processes: Generators and Their Potential Theory. World Scientific Publishing Company, 2002.

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40

Pseudo Differential Operators & Markov Processes: Markov Processes And Applications. Imperial College Press, 2005.

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41

Francesco, De Giovanni, and Newell Martin L. 1939-, eds. Infinite groups 1994: Proceedings of the international conference held in Ravello, Italy, May 23-27, 1994. Walter de Gruyter, 1996.

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42

(Editor), Vladimir Scheffer, and Jean E. Taylor (Editor), eds. Almgren's Big Regularity Paper: Q-Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-Minimizing Rectifiable Currents Up to Codimension ... Scientific Monograph Series in Mathematics). World Scientific Publishing Company, 2000.

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43

Landkof, N. S. Foundations of Modern Potential Theory. Brand: Springer, 2011.

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