In potential theory (the study of harmonic function) and functional analysis, Dirichlet forms generalize the Laplacian (the mathematical operator on scalar fields). Dirichlet forms can be defined on any measure space, without the need for mentioning partial derivatives. This allows mathematicians to study the Laplace equation and heat equation on spaces that are not manifolds, for example, fractals. The benefit on these spaces is that one can do this without needing a gradient operator, and in particular, one can even weakly define a "Laplacian" in this manner if starting with the Dirichlet form.
and functional analysis, Dirichletforms generalize the Laplacian (the mathematical operator on scalar fields). Dirichletforms can be defined on any measure...
In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted Dir ( α ) {\displaystyle \operatorname...
Lejeune Dirichlet (1805–1859). In finite-element analysis, the essential or Dirichlet boundary condition is defined by weighted-integral form of a differential...
In mathematics, a Dirichlet series is any series of the form ∑ n = 1 ∞ a n n s , {\displaystyle \sum _{n=1}^{\infty }{\frac {a_{n}}{n^{s}}},} where s is...
theory) Dirichlet eigenvalue Dirichlet's ellipsoidal problem Dirichlet eta function (number theory) DirichletformDirichlet function (topology) Dirichlet hyperbola...
Johann Peter Gustav Lejeune Dirichlet (German: [ləˈʒœn diʁiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician. In number theory, he proved...
Z → C {\displaystyle \chi :\mathbb {Z} \rightarrow \mathbb {C} } is a Dirichlet character of modulus m {\displaystyle m} (where m {\displaystyle m} is...
commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the...
In natural language processing, latent Dirichlet allocation (LDA) is a Bayesian network (and, therefore, a generative statistical model) for modeling...
In probability theory, Dirichlet processes (after the distribution associated with Peter Gustav Lejeune Dirichlet) are a family of stochastic processes...
Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons...
the associated Dirichletform operator. This result means that if a function is in the range of the exponential of the Dirichletform operator—which means...
learning, the hierarchical Dirichlet process (HDP) is a nonparametric Bayesian approach to clustering grouped data. It uses a Dirichlet process for each group...
original on 31 July 2020. Apostol, Tom M. (1990), Modular functions and Dirichlet Series in Number Theory, New York: Springer-Verlag, ISBN 0-387-97127-0...
{\displaystyle L(1,\chi )} . Dirichlet also showed that the L-series can be written in a finite form, which gives a finite form for the class number. Suppose...
In mathematics, Maass forms or Maass wave forms are studied in the theory of automorphic forms. Maass forms are complex-valued smooth functions of the...
are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral...
and Dirichlet Series in Number Theory", New York: Springer-Verlag 2nd Ed. Ashworth, M. H. (1968), Congruence and identical properties of modular forms (D...
the field of mathematical analysis, a general Dirichlet series is an infinite series that takes the form of ∑ n = 1 ∞ a n e − λ n s , {\displaystyle \sum...
used in the theory of partial differential equations for solving the Dirichlet and Neumann boundary value problems for the Laplacian in a bounded domain...
Hypercontractivity and logarithmic Sobolev inequalities for the Clifford Dirichletform. Duke Math. J. 42 (1975), no. 3, 383–396. Gross, Leonard: Existence...
In mathematics, the Dirichlet convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory...
"Hypercontractivity and logarithmic Sobolev inequalities for the Clifford-Dirichletform", Duke Journal of Mathematics, 42 (3): 383–396, doi:10.1215/S0012-7094-75-04237-4...
begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions...
in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number...
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