In the first half of the thesis I investigate David Hilbert's early ontology of mathematics around the period 1899-1916. Hilbert's early views are of significant philosophical interest and have been largely ignored due to his later, more influential work. I suggest that, in this period Hilbert, can be understood as an early structuralist. In the second half of the thesis, I connect two important debates in the foundations of mathematics: Hale and Wright's neo-Fregean logicism and the Frege-Hilbert controversy. Using this connection, I adapt Frege's objections to Hilbert and apply them to Hale and Wright's account. By doing this, I show that the neo-Fregean logicists have long abandoned the Fregean element of their program in favor of a structuralist ontology. I conclude that our ontological conception of what exists in mathematics and what it is like constrains the foundations we use to characterise mathematical reality.

Orientador : Prof. Dr. Alexandre Kirilov / Dissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Matemática. Defesa: Curitiba, 26/02/2016 / Inclui referências : f. 48-49 / Área de concentração: Matematica / Resumo: A partir do conceito de operadores invariantes em relação a uma decomposição de um espaço de Hilbert em subespaços de dimensão finita, introduzimos o símbolo do operador em relação a essa decomposição. Esse símbolo é uma sequência de matrizes cujas propriedades permitem, por exemplo, afirmar se o operador está em alguma classe de Schatten-von Neumann e se é possível estende-lo a um operador limitado. Usamos esses resultados para decompor o espaço de Hilbert L2(M), sobre uma variedade suave compacta orientavel sem bordo M, como soma direta de autoespaços de um operador diferencial el?tico autoadjunto positivo e estudamos propriedades que os operadores invariantes possuem neste espaço. Por fim, obtemos resultados acerca da hipoeliticidade Global de operadores invariantes sobre M analisando seu símbolo. / Abstract: From the idea of invariant operators relative to a fixed partition of a Hilbert space into a direct sum of finite dimensional subspaces, we introduce the operator's symbol relative to this decomposition. This symbol is a sequence of matrices whose properties allow us, for example, to state if the operator belong to some Schatten-von Neumann class and if it can be extended to a bounded operator. We apply this results to decompose the Hilbert space L2(M), where M is a orientable compact smooth manifold without boundary, as direct sum of eigenspaces of a positive self-adjoint elliptic differential operator and then we study some properties that the invariants operators have in this space. Finally, we obtain results about global hypoellipticity of invariant operators on M analyzing their symbol.

Made available in DSpace on 2015-05-15T11:46:22Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 776829 bytes, checksum: 5e5618b1edaa3e5c19d7d38daebb104e (MD5) Previous issue date: 2014-02-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Our goal in this work is to present beautiful results due to Huckaba-Marley concerning the Hilbert coefficients of an ideal of finite co-length in a Cohen-Macaulay local ring, as well as the depth of its associated graded ring. For this end, we employ the Huckaba- Marley complex, which is a fundamental tool for the obtainment of the main theorem discussed herein. / Nosso objetivo neste trabalho é apresentar os belos resultados de Huckaba-Marley sobre os coeficientes de Hilbert de um ideal de co-comprimento nito em um anel local Cohen-Macaulay, bem como a profundidade do seu anel graduado associado. Para tal, aplicamos o complexo de Huckaba-Marley, ferramenta fundamental na obtenção do teorema principal aqui discutido.

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This paper will be mostly concerned with matrices of infinite order with elements which lie in Hilbert Space. All the properties of real and complex numbers and all the properties of infinite series and infinite sequences that are not listed will be assumed.

This thesis is a study of fundamental properties of Hilbert space, properties of linear manifold, and realizations of Hilbert space.

Orientador: Hu Sheng / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-17T05:41:56Z (GMT). No. of bitstreams: 1 QuadrosNeto_MatiasJose_M.pdf: 1186131 bytes, checksum: d185a04e46065e464f124e38e4f0f3ed (MD5) Previous issue date: 1979 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática

Orientador: Jose Luiz Boldrini / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-19T10:58:48Z (GMT). No. of bitstreams: 1 Bonfim_LuciaResendePereira_M.pdf: 1568473 bytes, checksum: 9f17158e81a9dd55608b4071e38102be (MD5) Previous issue date: 1994 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática Aplicada

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In a 2005 paper, Yang constructed families of Hilbert Eisenstein series, which when restricted to the diagonal are conjecturedto span the underlying space of elliptic modular forms. Oneapproach to these conjectures is to show the non-vanishing of an innerproduct of elliptic eigenforms with the restrictions of Eisensteinseries. In this paper, we compute this inner product locally by usingexplicit values of new vectors in the Waldspurger model.