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Journal articles on the topic 'Multiplicative convolution'

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Published: 4 June 2021
Last updated: 27 April 2022

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1

Bercovici, Hari. "Multiplicative monotonic convolution." Illinois Journal of Mathematics 49, no. 3 (July 2005): 929–51. http://dx.doi.org/10.1215/ijm/1258138229.

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2

Gao, Mingchu. "On bi-free multiplicative convolution." Studia Mathematica 248, no. 2 (2019): 129–46. http://dx.doi.org/10.4064/sm171024-4-5.

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3

Popa, Mihai, and Jiun-Chau Wang. "On multiplicative conditionally free convolution." Transactions of the American Mathematical Society 363, no. 12 (December 1, 2011): 6309–35. http://dx.doi.org/10.1090/s0002-9947-2011-05242-6.

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4

Kieburg, Mario. "Additive matrix convolutions of Pólya ensembles and polynomial ensembles." Random Matrices: Theory and Applications 09, no. 04 (November 8, 2019): 2150002. http://dx.doi.org/10.1142/s2010326321500027.

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Recently, subclasses of polynomial ensembles for additive and multiplicative matrix convolutions were identified which were called Pólya ensembles (or polynomial ensembles of derivative type). Those ensembles are closed under the respective convolutions and, thus, build a semi-group when adding by hand a unit element. They even have a semi-group action on the polynomial ensembles. Moreover, in several works transformations of the bi-orthogonal functions and kernels of a given polynomial ensemble were derived when performing an additive or multiplicative matrix convolution with particular Pólya ensembles. For the multiplicative matrix convolution on the complex square matrices the transformations were even done for general Pólya ensembles. In the present work, we generalize these results to the additive convolution on Hermitian matrices, on Hermitian anti-symmetric matrices, on Hermitian anti-self-dual matrices and on rectangular complex matrices. For this purpose, we derive the bi-orthogonal functions and the corresponding kernel for a general Pólya ensemble which was not done before. With the help of these results, we find transformation formulas for the convolution with a fixed matrix or a random matrix drawn from a general polynomial ensemble. As an example, we consider Pólya ensembles with an associated weight which is a Pólya frequency function of infinite order. But we also explicitly evaluate the Gaussian unitary ensemble as well as the complex Laguerre (aka Wishart, Ginibre or chiral Gaussian unitary) ensemble. All results hold for finite matrix dimension. Furthermore, we derive a recursive relation between Toeplitz determinants which appears as a by-product of our results.
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5

Belinschi, S. T., and H. Bercovici. "Hinčin's Theorem for Multiplicative Free Convolution." Canadian Mathematical Bulletin 51, no. 1 (March 1, 2008): 26–31. http://dx.doi.org/10.4153/cmb-2008-004-3.

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AbstractHinčin proved that any limit law, associated with a triangular array of infinitesimal random variables, is infinitely divisible. The analogous result for additive free convolution was proved earlier by Bercovici and Pata. In this paper we will prove corresponding results for the multiplicative free convolution of measures defined on the unit circle and on the positive half-line.
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6

Bormetti, Giacomo, and Sofia Cazzaniga. "Multiplicative noise, fast convolution and pricing." Quantitative Finance 14, no. 3 (November 16, 2012): 481–94. http://dx.doi.org/10.1080/14697688.2012.729857.

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7

Haraoka, Yoshishige. "Multiplicative middle convolution for KZ equations." Mathematische Zeitschrift 294, no. 3-4 (May 14, 2019): 1787–839. http://dx.doi.org/10.1007/s00209-019-02322-9.

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8

Astola, Jaakko. "Multiplicative complexity, convolution, and the DFT." Signal Processing 20, no. 1 (May 1990): 95. http://dx.doi.org/10.1016/0165-1684(90)90081-9.

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9

Leake, Jonathan, and Nick Ryder. "Connecting the q-multiplicative convolution and the finite difference convolution." Advances in Mathematics 374 (November 2020): 107334. http://dx.doi.org/10.1016/j.aim.2020.107334.

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10

LE, T. A., and J. W. SANDER. "CONVOLUTIONS OF RAMANUJAN SUMS AND INTEGRAL CIRCULANT GRAPHS." International Journal of Number Theory 08, no. 07 (August 28, 2012): 1777–88. http://dx.doi.org/10.1142/s1793042112501023.

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There exist several generalizations of the classical Dirichlet convolution, for instance the so-called A-convolutions analyzed by Narkiewicz. We shall connect the concept of A-convolutions satisfying a weak form of regularity and Ramanujan sums with the spectrum of integral circulant graphs. These generalized Cayley graphs, having circulant adjacency matrix and integral eigenvalues, comprise a great amount of arithmetical features. By use of our concept we obtain a multiplicative decomposition of the so-called energy of integral circulant graphs with multiplicative divisor sets. This will be fundamental for the study of open problems, in particular concerning the detection of integral circulant graphs with maximal or minimal energy.
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11

Cébron, Guillaume. "Matricial model for the free multiplicative convolution." Annals of Probability 44, no. 4 (July 2016): 2427–78. http://dx.doi.org/10.1214/15-aop1024.

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12

Salekhova, Layla, and Elvira Chebotareva. "On a class of multiplicative-convolution equations." International Journal of Mathematical Analysis 8 (2014): 495–501. http://dx.doi.org/10.12988/ijma.2014.4254.

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13

Spector, Donald. "Multiplicative functions, Dirichlet convolution, and quantum systems." Physics Letters A 140, no. 6 (October 1989): 311–16. http://dx.doi.org/10.1016/0375-9601(89)90626-9.

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14

Haukkanen, Pentti. "Derivation of arithmetical functions under the Dirichlet convolution." International Journal of Number Theory 14, no. 05 (May 28, 2018): 1257–64. http://dx.doi.org/10.1142/s1793042118500781.

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We present the group-theoretic structure of the classes of multiplicative and firmly multiplicative arithmetical functions of several variables under the Dirichlet convolution, and we give characterizations of these two classes in terms of a derivation of arithmetical functions.
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15

Laohakosol, Vichian, and Nittiya Pabhapote. "Completely multiplicative functions arising from simple operations." International Journal of Mathematics and Mathematical Sciences 2004, no. 9 (2004): 431–41. http://dx.doi.org/10.1155/s0161171204304163.

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Given two multiplicative arithmetic functions, various conditions for their convolution, powers, and logarithms to be completely multiplicative, based on values at the primes, are derived together with their applications.
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16

Avsyankin, O. G. "An algebra generated by multiplicative discrete convolution operators." Russian Mathematics 55, no. 1 (January 2011): 1–6. http://dx.doi.org/10.3103/s1066369x11010014.

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17

Salekhov, L. G., and L. L. Salekhova. "The unique solvability of certain multiplicative-convolution equations." Russian Mathematics 56, no. 5 (April 17, 2012): 57–60. http://dx.doi.org/10.3103/s1066369x12050076.

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18

Bernal-Gonzalez, Luis, J. Alberto Conejero, George Costakis, and Juan B. Seoane-Sepulveda. "Multiplicative structures of hypercyclic functions for convolution operators." Journal of Operator Theory 80, no. 1 (July 2018): 213–24. http://dx.doi.org/10.7900/jot.2017sep27.2162.

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19

Sakuma, Noriyoshi, and Hiroaki Yoshida. "New limit theorems related to free multiplicative convolution." Studia Mathematica 214, no. 3 (2013): 251–64. http://dx.doi.org/10.4064/sm214-3-4.

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20

Avsyankin, Oleg Gennadievich, and Alisa Markovna Koval’chuk. "Multiplicative Discrete Convolution Operators with Complex Conjugate Operator." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 2 (2016): 17–21. http://dx.doi.org/10.18522/0321-3005-2016-2-17-21.

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21

Rojas-León, Antonio. "Explicit local multiplicative convolution of $\ell$-adic sheaves." Revista Matemática Iberoamericana 34, no. 3 (August 27, 2018): 1373–86. http://dx.doi.org/10.4171/rmi/1027.

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22

Pitas, I., and M. Strintzis. "Multidimensional cyclic convolution algorithms with minimal multiplicative complexity." IEEE Transactions on Acoustics, Speech, and Signal Processing 35, no. 3 (March 1987): 384–90. http://dx.doi.org/10.1109/tassp.1987.1165132.

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23

Vogt, Dietmar. "$\mathcal{E}'$ as an algebra by multiplicative convolution." Functiones et Approximatio Commentarii Mathematici 59, no. 1 (September 2018): 117–28. http://dx.doi.org/10.7169/facm/1719.

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24

Marcus, Adam W., Daniel A. Spielman, and Nikhil Srivastava. "Finite free convolutions of polynomials." Probability Theory and Related Fields 182, no. 3-4 (February 18, 2022): 807–48. http://dx.doi.org/10.1007/s00440-021-01105-w.

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AbstractWe study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric additive and multiplicative convolutions were introduced by Walsh and Szegö in different contexts, and have been studied for a century. The asymmetric additive convolution, and the connection of all of them with random matrices, is new. By developing the analogy with free probability, we prove that these convolutions produce real rooted polynomials and provide strong bounds on the locations of the roots of these polynomials.
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25

Ueda, Yuki. "Max-convolution semigroups and extreme values in limit theorems for the free multiplicative convolution." Bernoulli 27, no. 1 (February 2021): 502–31. http://dx.doi.org/10.3150/20-bej1247.

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26

Zhong, Ping. "On Regularity for Measures in Multiplicative Free Convolution Semigroups." Complex Analysis and Operator Theory 7, no. 4 (April 10, 2012): 1337–43. http://dx.doi.org/10.1007/s11785-012-0231-0.

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27

Zhong, Ping. "Free Brownian motion and free convolution semigroups: multiplicative case." Pacific Journal of Mathematics 269, no. 1 (July 15, 2014): 219–56. http://dx.doi.org/10.2140/pjm.2014.269.219.

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28

Haukkanen, Pentti. "Some characterizations of totients." International Journal of Mathematics and Mathematical Sciences 19, no. 2 (1996): 209–17. http://dx.doi.org/10.1155/s0161171296000312.

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An arithmetical function is said to be a totient if it is the Dirichlet convolution between a completely multiplicative function and the inverse of a completely multiplicative function. Euler's phi-function is a famous example of a totient. All completely multiplicative functions are also totients. There is a large number of characterizations of completely multiplicative functions in the literature, while characterizations of totients have not been widely studied in the literature. In this paper we present several arithmetical identities serving as characterizations of totients. We also introduce a new concrete example of a totient.
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29

Bercovici, Hari, and Dan-Virgil Voiculescu. "Lévy-Hinčin type theorems for multiplicative and additive free convolution." Pacific Journal of Mathematics 153, no. 2 (April 1, 1992): 217–48. http://dx.doi.org/10.2140/pjm.1992.153.217.

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30

Kieburg, Mario, Peter J. Forrester, and Jesper R. Ipsen. "Multiplicative convolution of real asymmetric and real anti-symmetric matrices." Advances in Pure and Applied Mathematics 10, no. 4 (October 1, 2019): 467–92. http://dx.doi.org/10.1515/apam-2018-0037.

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AbstractThe singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a polynomial ensemble. It is furthermore the case that the corresponding bi-orthogonal system can be determined in terms of Meijer G-functions, and the correlation kernel given as an explicit double contour integral. It has recently been shown that the Hermitised product {X_{M}\cdots X_{2}X_{1}AX_{1}^{T}X_{2}^{T}\cdots X_{M}^{T}}, where each {X_{i}} is a standard real Gaussian matrix and A is real anti-symmetric, exhibits analogous properties. Here we use the theory of spherical functions and transforms to present a theory which, for even dimensions, includes these properties of the latter product as a special case. As an example we show that the theory also allows for a treatment of this class of Hermitised product when the {X_{i}} are chosen as sub-blocks of Haar distributed real orthogonal matrices.
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31

Salekhova, Leila, and Elvira Chebotareva. "Regular solutions of multiplicative-convolution equation in the Vladimirov algebra." International Journal of Mathematical Analysis 9 (2015): 2681–88. http://dx.doi.org/10.12988/ijma.2015.59241.

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32

Huang, Hao-Wei, and Ping Zhong. "On the supports of measures in free multiplicative convolution semigroups." Mathematische Zeitschrift 278, no. 1-2 (April 18, 2014): 321–45. http://dx.doi.org/10.1007/s00209-014-1317-3.

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33

Crawley-Boevey, William, and Peter Shaw. "Multiplicative preprojective algebras, middle convolution and the Deligne–Simpson problem." Advances in Mathematics 201, no. 1 (March 2006): 180–208. http://dx.doi.org/10.1016/j.aim.2005.02.003.

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34

Zagorodnyuk, А. V., and V. V. Kravtsiv. "Multiplicative Convolution on the Algebra of Block-Symmetric Analytic Functions." Journal of Mathematical Sciences 246, no. 2 (February 28, 2020): 245–55. http://dx.doi.org/10.1007/s10958-020-04734-z.

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35

Szczepański, Jerzy. "A remark on the distribution of products of independent normal random variables." Science, Technology and Innovation 10, no. 3 (March 10, 2021): 30–37. http://dx.doi.org/10.5604/01.3001.0014.7861.

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We present a proof of the explicit formula of the probability density function of the product of normally distributed independent random variables using the multiplicative convolution formula for Meijer G functions.
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36

Morgera, Salvatore D. "Multiplicative complexity of bilinear algorithms for cyclic convolution over finite fields." Multidimensional Systems and Signal Processing 1, no. 1 (March 1990): 99–111. http://dx.doi.org/10.1007/bf01812210.

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37

Gebremeskel, Kibrom G., and Lin Zhe Huang. "Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions." Acta Mathematica Sinica, English Series 35, no. 8 (April 18, 2019): 1300–1310. http://dx.doi.org/10.1007/s10114-019-8329-1.

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38

Belinschi, Serban Teodor. "The Atoms of the Free Multiplicative Convolution of Two Probability Distributions." Integral Equations and Operator Theory 46, no. 4 (August 2003): 377–86. http://dx.doi.org/10.1007/s00020-002-1145-4.

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39

Kołodziejek, Bartosz, and Kamil Szpojankowski. "A phase transition for tails of the free multiplicative convolution powers." Advances in Mathematics 403 (July 2022): 108398. http://dx.doi.org/10.1016/j.aim.2022.108398.

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40

Téllez, Manuel A. Aguirre. "A convolution product of(2j)th derivative of Dirac's delta inrand multiplicative distributional product betweenr−kand∇(△jδ)." International Journal of Mathematics and Mathematical Sciences 2003, no. 13 (2003): 789–99. http://dx.doi.org/10.1155/s0161171203110289.

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The purpose of this paper is to obtain a relation between the distributionδ(2j)(r)and the operator△jδand to give a sense to the convolution distributional productδ(2j)(r)∗δ(2s)(r)and the multiplicative distributional productsr−k⋅∇(△jδ)and(r−c)−k⋅∇(△jδ).
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41

Pabhapote, Nittiya, and Vichian Laohakosol. "Combinatorial Aspects of the Generalized Euler's Totient." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–15. http://dx.doi.org/10.1155/2010/648165.

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A generalized Euler's totient is defined as a Dirichlet convolution of a power function and a product of the Souriau-Hsu-Möbius function with a completely multiplicative function. Two combinatorial aspects of the generalized Euler's totient, namely, its connections to other totients and its relations with counting formulae, are investigated.
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42

Garina, Marina I. "Multiplicative convolution application to attributes having both negative and positive utility values." SPIIRAS Proceedings 3, no. 22 (March 17, 2014): 176. http://dx.doi.org/10.15622/sp.22.9.

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43

Belinschi, Serban T., and Alexandru Nica. "On a remarkable semigroup of homomorphisms with respect to free multiplicative convolution." Indiana University Mathematics Journal 57, no. 4 (2008): 1679–714. http://dx.doi.org/10.1512/iumj.2008.57.3285.

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44

Speicher, Roland. "Multiplicative functions on the lattice of non-crossing partitions and free convolution." Mathematische Annalen 298, no. 1 (January 1994): 611–28. http://dx.doi.org/10.1007/bf01459754.

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45

Chernega, Irina, Pablo Galindo, and Andriy Zagorodnyuk. "A multiplicative convolution on the spectra of algebras of symmetric analytic functions." Revista Matemática Complutense 27, no. 2 (June 2, 2013): 575–85. http://dx.doi.org/10.1007/s13163-013-0128-0.

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46

Laohakosol, Vichian, and Nittiya Pabhapote. "Properties of rational arithmetic functions." International Journal of Mathematics and Mathematical Sciences 2005, no. 24 (2005): 3997–4017. http://dx.doi.org/10.1155/ijmms.2005.3997.

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Rational arithmetic functions are arithmetic functions of the formg1∗⋯∗gr∗h1−1∗⋯∗hs−1, wheregi,hjare completely multiplicative functions and∗denotes the Dirichlet convolution. Four aspects of these functions are studied. First, some characterizations of such functions are established; second, possible Busche-Ramanujan-type identities are investigated; third, binomial-type identities are derived; and finally, properties of the Kesava Menon norm of such functions are proved.
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47

Avsyankin, O. G. "On the C*-algebra generated by multiplicative discrete convolution operators with oscillating coefficients." Siberian Mathematical Journal 55, no. 6 (November 2014): 977–83. http://dx.doi.org/10.1134/s0037446614060019.

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48

Zhong, Ping. "On the Free Convolution with a Free Multiplicative Analogue of the Normal Distribution." Journal of Theoretical Probability 28, no. 4 (May 16, 2014): 1354–79. http://dx.doi.org/10.1007/s10959-014-0556-x.

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49

Téllez, M. A. Aguirre. "The product of convolution Pλ± ∗ Pμ∓ and the multiplicative product Pλ± · δκ(P±)." Mathematical and Computer Modelling 23, no. 10 (May 1996): 135–44. http://dx.doi.org/10.1016/0895-7177(96)00059-3.

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50

Patie, Pierre, and Anna Srapionyan. "Self-similar cauchy problems and generalized Mittag-Leffler functions." Fractional Calculus and Applied Analysis 24, no. 2 (April 1, 2021): 447–82. http://dx.doi.org/10.1515/fca-2021-0020.

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Abstract By observing that the fractional Caputo derivative of order α ∈ (0, 1) can be expressed in terms of a multiplicative convolution operator, we introduce and study a class of such operators which also have the same self-similarity property as the Caputo derivative. We proceed by identifying a subclass which is in bijection with the set of Bernstein functions and we provide several representations of their eigenfunctions, expressed in terms of the corresponding Bernstein function, that generalize the Mittag-Leffler function. Each eigenfunction turns out to be the Laplace transform of the right-inverse of a non-decreasing self-similar Markov process associated via the so-called Lamperti mapping to this Bernstein function. Resorting to spectral theoretical arguments, we investigate the generalized Cauchy problems, defined with these self-similar multiplicative convolution operators. In particular, we provide both a stochastic representation, expressed in terms of these inverse processes, and an explicit representation, given in terms of the generalized Mittag-Leffler functions, of the solution of these self-similar Cauchy problems. This work could be seen as an-in depth analysis of a specific class, the one with the self-similarity property, of the general inverse of increasing Markov processes introduced in [15].
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