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Mathematics and Statistics


Published Papers

Cho, Ilwoo (2017). Non-factorizable C-valued functions induced by finite connected graphs. Opuscula Math. Vol 37,2. Pp 225-263,

Ilwoo Cho and Palle E. T. Jorgensen (2017). Krein-space operators determined by free product algebras induced by primes and graphs. Spec. Matrices. 5:1-35.

Cho, Ilwoo (2015). Dynamical systems on arithmetic functions determined by primes. Banach J. Math. Anal. Vol 9,1. Pp 173--215. doi:10.15352/bjma/09-1-15.

Cho, Ilwoo and Jorgensen, Palle (2014). A Von Neumann Algebra Over the Adele Ring and the Euler Totient Function. Operator Theory. November. Pp. 1-47.

Dynamical Systems on Arithmetic Functions Determined by Primes, Apr., 2014, BJMA

An Application of Free Probability to Arithmetic functions,  Apr., 2014, CAOT (With Prof. Palle Jorgensen  DOI: 10.1007/s 11785-014-0378-y

Krein-Space Representations of Arithmetic Functions Determined by Primes,  Feb., 2014, ART  (With Prof. Palle Jorgensen)  DOI: 10.1007/s 10468-014-9473-z

Complex-Valued Functions Induced by Graphs, Feb., 2014  CAOT  DOI: 10.1007/s11785-014-0368-0

Actions of Arithmetic Functions on Matrices and Corresponding Representations, Dec., 2013, Ann. Funct. Anal.: Special Issues  (With Prof. Palle Jorgensen)

Arithmetic Functions in Harmonic Analysis and Operator Theory, Nov., 2013, Springer Book Project: Handbook of Operator Theory  (With Prof. Palle Jorgensen)

p-Adic Banach-Space Operators and Adelic Banach-Space Operators, Jun., 2013, Opuscula Math.

Classification on Arithmetic Functions and Corresponding Free-Moment L-Functions May, 2013, Bulletin of Korean Math. Soc.

Krein-Space Operators Induced by Dirichlet Characters, Apr., 2013 (With Prof. Palle Jorgensen) Special Issue of Contemporary Mathematics, American Mathematical Society

Free Distributional Data of Arithmetic Functions and Corresponding Generating Functions Determined by Gaps of Primes, Apr., 2013, CAOT, DOI: 10.1007/s11785-013-0311-9

Operators Induced by Prime Numbers, Jan., 2013, Methods and Appl. Anal (Methods Appl. Anal., 19, no 4, (2013) 313 - 340)

K-Groups of a C*-Algebra Generated by a Single Operator, Dec., 2012, CAOT, DOI: 10.1007/s11785-013-0285-7

The Index Semigroup and K-Groups of Graph-Groupoid C*-Algebras, Oct., 2012, CAOT, DOI: 10.1007/s11785-012-0271-5

Operator Algebras Induced by Monads, (With Prof. Palle Jorgensen) July 2012, JAMC

K-Theory Induced by a Single Partial Isometry, June 2012, Opuscula Math.

C*-Algebraic K-Theory Induced by Graphs, Mar. 2012, Americal J. Math. Math. Sci.

Operators Induced by Graphs, (With Prof. Palle Jorgensen) Jan. 2012, Letters in Math. Phy., DOI: 10.1007/s11005-012-0575-4 (Letters in Math. Phy., 102, Issue 3, (2012) 323 - 269)

Index Semigroup and Indexing on von Neumann Algebras, Nov. 2011, CAOT, DOI: 10.1007/s11785-011-0208-4

Operator-Algebraic Quotient Structures Induced by Graphs II, Oct., 2011, CAOT, DOI: 10.1007/s11785-011-0204-8

Algebras in Resistance Networks and Their Representations, (With Prof. Palle Jorgensen) Jul., 2011, Funct. Anal. & Other Math.

Symmetry in Tensor Algebras Over Hilbert Space, (With Prof. Palle Jorgensen) Jun., 2011, Illinois Journal of Math.

Free Probability on Operator Algebras Induced by Currents in Electric Resistance Networks, (With Prof. Palle Jorgensen) Jun., 2011, Internat. J. Funct. Anal & Oper. Theo.

Histories Distorted by Partial Isometries, May., 2011, J. Physical Math. DOI:10.4303/jpm/P110301 (J. Phy. Math., vol 3, (2011) article ID: P110301)

Entropy of Graphs and Information-Theoretical Characterization of Graphs with Fractal Property, May, 2011 Adv. Appl. Math. Sci.

Index-Morphism on Finite Trees and Classification of von Neumann Algebras Induced by Finite Trees, Apr. 2011 Invited Paper (Chapter) in a Book: "Quantum Mechanics," InTech Open Access Publisher

Free Probability Induced by Electric Resistance Networks on Energy Hilbert Spaces, (With Prof. Palle Jorgensen) Mar., 2011 Opuscula Math. (Opuscula Mathematica, 31, no. 4, (2011) 549 - 598)

Index on von Neumann Algebras Induced by Graphs. Jan. 2011 Appl. Math. Sci.

Graph-Matrices and Matricial Graph C*-Algebras, Dec., 2010 B. of KMS

Measure-Framing on Graphs, and Corresponding von Neumann Algebras, Nov., 2010 AM

Fractals in Von Neumann Algebras, Aug., 2010 AM

Moment Computations of Graphs with Fractal Property, (With Prof. Palle Jorgensen) Aug., 2010, JAMC DOI: 10.1007/s12190-010-0440-5 (J. Appl. Math. Comput., 37, (2011) 377 - 406)

Frames, Fractals and Radial Operators in Hilbert Space, Aug., 2010, JMSAA (J. Math. Sci.: Adv. Appl., vol. 5, no. 2, (2010) 333 - 393)

Graph Fractaloids: Classification and Application of Graph Groupoids with Fractal Property, Jul., 2010, Book: Classification and Application of Fractals NOVA Publisher

Towers of von Neumann Algebras Induced by Graphs, Jul., 2010, Oriental J. Math.

Directed Graphs, von Neumann Algebras, and Index, (With Prof. Palle Jorgensen) Jun., 2010, ART DOI: 10.1007/s10468-010-9233-7 (Alg. Rep. Theo, Vol 15, issue 1, (2012) 53 - 108)

Diagram Groupoids and von Neumann Algebras, Jun., 2010, CAOT, DOI: 10.1007/s11785-010-0103-4, (Compl. Anal. Oper. Theo, 6, (2012) 843 - 895)

Group-Framing and Corresponding von Neumann Algebras, Mar., 2010, AAMS, (Adv. Appl. Math Sci., 2, vol. 5, (2010) 111 - 164)

Free Graph Stochastic Processes, Sep., 2009, JAMI

C*-Dynamical Systems Induced by Partial Isometries, (With Prof. Palle Jorgensen) June, 2009, AAMS (Adv. & Appl. Math Sci., 1 vol. 2, (2010) 21 - 59)

Fractal Property in B(H) Induced by Partial Isometries, Apr., 2009, CAOT, DOI:10.1007/s11785-009-0035-z (Compl. Anal. Oper. Theo. 5, no. 1, (2011) 1 - 40)

Application of Automata and Graphs: Labeling Operators in Hilbert Space II, (With Prof. Palle Jorgensen) Mar., 2009, JMP DOI:10.1063/1.3141524

Graph-Matrices over Additive Graph Groupoids, Jan., 2009, JAMC

C*-Subalgebras Generated by a Single Operatort in B(H), (With Prof. Palle Jorgensen) Dec., 2008, ACTA. Appl. Math: Special Issues DOI:10.1007/s10440-009-9478-5 (ACTA Appl. Math, 108, (2009) 625 - 664)

Graph Groupoids and Corresponding Representations, Dec., 2008, NOVA Publisher (Invited Paper) Group Theory: Classes, Representations and Connections, and Applications, ISBN: 978-1-60876-175-3

Von Neumann Algebras Generated by Automata, Dec. 2008, NOVA Publisher (Invited Paper) Graphene: Research, Technology and Applications ISBN: 978-1-60692-666-6

Application of Automata and Graphs: Labeling Operators in Hilbert Space I, (With Prof. Palle Jorgensen) Oct., 2008, ACTA Appl. Math: Special Issues DOI: 10.1063/1.3141524

Scalar-Valued Free Probability on a Graph von Neumann Algebra, Oct., 2008, J. of KMS. DOI: 10.4134/JKMS.2010.47.3.601, (J. Korean Math. Soc., 47, no 3, (2010) 601 - 631)

Vertex-Compressed Algebras in a Graph von Neumann Algebra, Aug., 2008, ACTA Appl. Math, DOI: 10.1007/s10440-008-9314-3 (ACTA Appl. Math., 108, no. 2, 315 - 351)

C*-Subalgebras Generated by Partial Isometries, (With Prof. Palle Jorgensen) Aug., 2008, JMP, DOI: 10.1063/1.3056588

Operator Algebraic Quotient Structures Induced by Directed Graphs, Mar., 2008, CAOT, DOI: 10.1007/s11785-008-0065-y

Group Freeness and Certain Amalgamated Freeness, Nov., 2007, JKMS (J. of KMS, 45, no. 3, (2008) 597 - 609)

C*-Algebras Generated by Partial Isometries, (With Prof. Palle Jorgensen) Sep., 2007, JAMC, (JAMC, 26, (2008) 1 - 48)

Measures on Graphs and Certain Groupoid Measures, Aug., 2007, CAOT (Compl. Anal. Oper. Theory, 2, (2008) 1 - 28)

Characterization of the Amalgamated Free Blocks of a Graph von Neumann Algebra, Mar., 2007, CAOT (Compl. Anal. Oper. Theory, 1, (2007) 367-398)

The Moments of Certain Perturbed Operators of the Radial Operator in the Free Group Factor L(F_N), Feb. 2007, JAA (J. of analysis & Applications, vol. 5, no. 3, (2007) 137 - 165)

Direct Producted W*-Probability Spaces and Corresponding Amalgamated Free Stochastic Integration, Feb. 2007, Bulletin of Korean Math. Soc. (Bull. Korean Math. Soc. 44 (2007), No. 1, 131 - 150)

Strictly Free Additively Stable Random Variables, Nov., 2006, FEJMS.

Graph Von Neumann Algebras, Nov., 2006, ACTA Applied Math. (ACTA Appl Math, (2007) 95 95 - 134)