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Makarov
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31	HARMONIC MEASURE AND POLYNOMIAL JULIA SETS I. BINDER, N. MAKAROV, AND S. SMIRNOV Abstract. There is a natural conjecture that the universal bounds for the dimension spectrum of harmonic measure are the same for simply co Add to Reading List Source URL: www.math.caltech.edu Language: English - Date: 2001-02-07 12:50:20 Fractals Julia set Ordinal numbers Set theory Diophantine approximation Symbol Holomorphic functional calculus Mathematical analysis Mathematics Mathematical logic
32	ON “THERMODYNAMICS” OF RATIONAL MAPS II. NON-RECURRENT MAPS N. MAKAROV AND S. SMIRNOV Abstract. The pressure function p(t) of a non-recurrent map is real analytic on some interval (0, t∗ ) with t∗ strictly greate Add to Reading List Source URL: www.math.caltech.edu Language: English - Date: 2001-10-02 17:46:58 Spectral theory Hilbert transform Koenigs function Mathematical analysis Operator theory Ordinary differential equations
33	AGGREGATION IN THE PLANE AND LOEWNER’S EQUATION L. CARLESON AND N. MAKAROV Abstract. We study an aggregation process which can be viewed as a deterministic analogue of the DLA model in the plane, or as a regularized ve Add to Reading List Source URL: www.math.caltech.edu Language: English - Date: 2001-02-07 12:47:00 Loewner differential equation Riemann zeta function Schramm–Loewner evolution Continuous function Partial differential equation Mathematical analysis Complex analysis Analytic number theory
34	ON ”THERMODYNAMICS” OF RATIONAL MAPS I. NEGATIVE SPECTRUM N. MAKAROV AND S. SMIRNOV Abstract. We study the pressure spectrum P (t) of the maximal measure for arbitrary rational maps. We also consider its modiﬁed ve Add to Reading List Source URL: www.math.caltech.edu Language: English - Date: 2001-02-07 12:45:10 Sobolev spaces Fourier analysis Operator theory Fractional calculus Vector space Continuous function Spectral theory of ordinary differential equations Holomorphic functional calculus Mathematics Algebra Mathematical analysis
35	LAPLACIAN PATH MODELS L. CARLESON AND N. MAKAROV 1. Introduction and results 1.1. Laplacian growth. In this paper we study two growth models in the complex plane – the needle and the geodesic η-models, deﬁned below. Add to Reading List Source URL: www.math.caltech.edu Language: English - Date: 2001-07-20 19:59:54 Complex analysis Loewner differential equation Geodesic
36	MEROMORPHIC INNER FUNCTIONS, TOEPLITZ KERNELS, AND THE UNCERTAINTY PRINCIPLE N. MAKAROV AND A. POLTORATSKI Introduction This paper touches upon several traditional topics of 1D linear complex analysis including distribut Add to Reading List Source URL: math.caltech.edu Language: English - Date: 2004-10-11 20:01:51 Fourier analysis Operator theory Ordinary differential equations Fourier transform Spectrum Hilbert transform Nevanlinna theory Spectral theory of ordinary differential equations Plancherel theorem for spherical functions Mathematical analysis Spectral theory Integral transforms
37	AGGREGATION IN THE PLANE AND LOEWNER’S EQUATION L. CARLESON AND N. MAKAROV Abstract. We study an aggregation process which can be viewed as a deterministic analogue of the DLA model in the plane, or as a regularized ve Add to Reading List Source URL: math.caltech.edu Language: English - Date: 2001-02-07 12:47:00 Loewner differential equation Riemann zeta function Schramm–Loewner evolution Continuous function Partial differential equation Mathematical analysis Complex analysis Analytic number theory
38	ON ”THERMODYNAMICS” OF RATIONAL MAPS I. NEGATIVE SPECTRUM N. MAKAROV AND S. SMIRNOV Abstract. We study the pressure spectrum P (t) of the maximal measure for arbitrary rational maps. We also consider its modiﬁed ve Add to Reading List Source URL: math.caltech.edu Language: English - Date: 2001-02-07 12:45:10 Sobolev spaces Fourier analysis Operator theory Fractional calculus Vector space Continuous function Spectral theory of ordinary differential equations Holomorphic functional calculus Mathematics Algebra Mathematical analysis
39	ON “THERMODYNAMICS” OF RATIONAL MAPS II. NON-RECURRENT MAPS N. MAKAROV AND S. SMIRNOV Abstract. The pressure function p(t) of a non-recurrent map is real analytic on some interval (0, t∗ ) with t∗ strictly greate Add to Reading List Source URL: math.caltech.edu Language: English - Date: 2001-10-02 17:46:58 Spectral theory Hilbert transform Koenigs function Mathematical analysis Operator theory Ordinary differential equations
40	FINE STRUCTURE OF HARMONIC MEASURE Nikolai G. Makarov California Institute of Technology Introduction Add to Reading List Source URL: math.caltech.edu Language: English - Date: 2001-02-06 20:01:20 Ordinal number Constructible universe Continuous function Diophantine approximation Dyadic cubes Dirac delta function Mathematical analysis Mathematics Operator theory