From operator theory to orthogonal polynomials combinatorics and number theory : a volume in Honor of Lance Littlejohns 70th birthday The main topics of this volume dedicated to Lance Littlejohn are operator and spectral theory orthogonal polynomials combinatorics number theory and the various interplays of these subjects. Although the event originally scheduled as the Baylor Analysis Fest had to be postponed due to the pandemic scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians. Contributors are: G.E. Andrews B.M. Brown D. Damanik M.L. Dawsey W.D. Evans J. Fillman D. Frymark A.G. García L.G. Garza F. Gesztesy D. Gómez Ullate Y. Grandati F.A. Grünbaum S. Guo M. Hunziker A. Iserles T.F. Jones K. Kirsten Y. Lee C. Liaw F. Marcellán C. Markett A. Martinez Finkelshtein D. McCarthy R. Milson D. Mitrea I. Mitrea M. Mitrea G. Novello D. Ong K. Ono J.L. Padgett M.M.M. Pang T. Poe A. Sri Ranga K. Schiefermayr Q. Sheng B. Simanek J. Stanfill L. Velázquez M. Webb J. Wilkening I.G. Wood M. Zinchenko. Preface Compositions and Chebyshev Polynomials Non negative Extensions of Hamiltonian Systems On Simon’s Hausdorff Dimension Conjecture Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures Ballistic Transport for Periodic Jacobi Operators on Zd Perspectives on General Left Definite Theory Sampling in the range of the analysis operator of a continuous frame having unitary structure An extension of the coherent pair of measures of the second kind on the unit circle Bessel Type Operators and a Refinement of Hardy’s Inequality Spectral Theory of Exceptional Hermite Polynomials Occupation time for classical and quantum walks On foci of ellipses inscribed in cyclic polygons A Differential Analogue of Favard’s Theorem Intrinsic properties of strongly continuous fractional semigroups in normed vector spaces The BFK gluing formula for zeta determinants and the conformal rescaling of a metric New representations of the Laguerre–Sobolev and Jacobi–Sobolev orthogonal polynomials Compactness or Lack Thereof for the Harmonic Double Layer Weighted Chebyshev Polynomials on Compact Subsets of the Complex Plane The Eichler integral of E2 and q brackets of t hook functions.