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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 26 for “"Holomorphic functions"”.
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The Boundary Behavior of Holomorphic Functions
… problems, the Lindel\"{o}f principle, and inner functions have been well studied for strongly pseudoconvex domains. In this thesis, we are going to study more generalized domains, those of finite type. In Chapter 2 we show that there is no Fatou's theorem for approach regions complex tangentially …
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Maximality of algebras of holomorphic functions
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1960.
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Interpolation of Weighted L2 Holomorphic Functions in Higher Dimensions
This thesis considers an interpolation theorem in the setting of several complex variables. We consider a Kahler manifold X with a metric &ohgr; whose Ricci curvature is non-positive and we assume that X admits a Green's function. In this setup we give a sufficient condition for a closed smooth …
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Methods of Complex Function Theory in Some Problems of Analysis: KMS States and Corona Problem
… surveys a pair of topics which both depend on holomorphic functions and Banach Algebras. Firstly, the prerequisite background knowledge common to both such as holomorphic functions, Banach spaces and algebras, and module theory is provided. Secondly, KMS states arising on Cuntz-Krieger algebras …
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On the Integrability of Derivatives of Holomorphic and M-Subharmonic Inner Functions In the Unit Ball of Cn
… Bn be the unit ball in Cn. If f is a bounded holomorphic function, we say that f is inner provided that its modulus has a radial limit of 1 almost everywhere on Sn where Sn is the unit sphere.</p> <p>If a > -1 and p > 0 then Apa denotes the weighted Bergman space of all holomorphic functions …
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Domains of convergence in infinite dimensional holomorphy
For certain subsets F(R) of holomorphic functions on a Reinhardt domain R in a Banach sequence space X, mainly for H_{\infty}(R), P^m(X) and P(X), we give precise descriptions of the domain of convergence dom F(R), i.e. the set of all points of R where the monomial expansion \sum_{\alpha\in …
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The strict typology : theory, generalizations and applications
… the space of bounded complex-valued continuous functions Cb(X), on a locally compact Hausdorff space X, by Buck. It was found to have many applications in Approximation Theory, spectral synthesis, spaces of bounded holomorphic functions and multipliers of Banach Algebras.
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Multi-dimensional continuous wavelet transforms and generalized fourier transforms in Clifford analysis
… to higher dimension of the theory of holomorphic functions in the complex plane. The generalized holomorphic functions, known as monogenic functions, are null-solutions of the so-called Dirac operator, a first order rotationally invariant differential operator factorizing the Laplacian …
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Regularity of the Bergman Projection on Variants of the Hartogs Triangle
… projection from the space of square integrable functions onto the space of square integrable holomorphic functions on a domain. Initially, the projection is defined on the L2 space, but its behavior on other function spaces, e.g. Lp, Sobolev and Holder spaces, is of considerable interest.In this …
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Isometries of Besov Type Spaces among Composition Operators
… for p >1 and alpha >1 be the Besov type space of holomorphic functions on the unit disk D. Given Phi, a holomorphic self map of D, we show the composition operator CPhi is an isometry on Bp,alpha if and only if the weighted composition operator WPhiPhi, is an isometry on the weighted Bergman space …
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THE INDEX THEOREM FOR QUASI-TORI
The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the numbers of negative and positive eigenvalues of the associated hermitian form. In this thesis, this theorem is generalized to quasi-tori, i.e. connected …
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Holomorphic Hardy Space Representations for Convex Domains in Cn
<p>This thesis deals with Hardy Spaces of holomorphic functions for a domain in several complex variables, that is, when the complex dimension is greater than or equal to two. The results we obtain are analogous to well known theorems in one complex variable. The domains we are concerned with are …
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Schur-class of finitely connected planar domains: the test-function approach
… of the compact convex set of matrix-valued holomorphic functions with positive real part on a finitely-connected planar domain 𝐑 normalized to have value equal to the identity matrix at some prescribed point t₀ ∈ 𝐑. This leads to an integral representation for such functions more general …
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Local complex singularity exponents for isolated singularities
… local complex'singularity exponents (lcse) for holomorphic functions whose zero sets have only isolated singularities. For a given holomorphic function f defined on a neighborhood of the origin in C[to the power of]n, the lcse c[sub]0(f) is defined as the supremum of all positive real number …
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Poletsky-Stessin Hardy Spaces on the Unit Disk
<p>The holomorphic functions on the unit disk $\mathbb{D}$ in the complex plane $\mathbb{C}$ have a remarkable property: to know the values of a holomorphic function on $\mathbb{D}$ it suffices to know only its values on the unit circle $\mathbb{T}$. However not all holomorphic functions on …
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Invariant Frechet algebras on bounded symmetric domains
… Cn , and G be the largest connected group of biholomorphic automorphisms of D. The algebra C( D) of all continuous (not necessarily bounded) complex-valued functions on D with compact-open topology is a Frechet algebra. A closed subalgebra of C(D) is called an invariant algebra if it is closed …
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Multidimensional distributions and generalized Hilbert transforms in Clifford analysis
… multidimensional generalization of the theory of holomorphic functions in one complex variable and – at the same time – as a refinement of harmonic analysis. In this doctoral thesis we study some specific families of multidimensional distributions in the framework of Euclidean Clifford analysis, …
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Topics in Gauge/Gravity Duality
… and show the one-loop finiteness of two-point functions of bosonic fields. We then perform a Hamiltonian analysis and compare SU(2) string states with predictions from the conjectured Bethe equations. Furthermore, we show that, at least at tree-level, the two-body S-matrix is reflectionless. We …
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The Theory of Exponential Differential Equations
… exponential function and the Weierstrass p-functions. The theory consists of a description of the algebraic structure on the solution sets together with necessary and sufficient conditions for a system of equations to have solutions. These conditions are stated in terms of a dimension …
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The density of complex zeros of random sums
… to reduce the question to the evaluation of a holomorphic function of four correlated normal random variables. Their results were generalized by Ibragimov and Zeitouni to a wide class of distribution of coefficients. Recently, Vanderbei extended the results he obtained with Shepp to random sums …
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