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"This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated."

"The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following, spectral integrals and spectral decompositions of self-adjoint and normal operators, perturbations of self-adjointness and of spectra of self-adjoint operators, forms and operators, and self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension."

"This volume contains twenty-one solicited articles by speakers at the IWOTA 2009 workshop, ranging from expository surveys to original research papers. The contributions reflect recent developments in operator theory and its applications. Consistent with the topics of recent IWOTA meetings, IWOTA 2009 was designed as a comprehensive, inclusive conference covering all aspects of theoretical and applied operator theory, ranging from classical analysis, differential and integral equations, complex and harmonic analysis to mathematical physics, mathematical systems and control theory, signal processing and numerical analysis. "

"This book explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents a systematic rehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The theory developed within this book has potential applications in various branches of algebra, including homological algebra, ring theory and K-theory. "

"Telah dilakukan inversi Elastic Impedance dan Dekomposisi Spektral pada lapangan Penobscot, untuk mengidentifikasi reservoir pada lapisan tipis. Perkembangan atribut seismik dewasa ini sangat membantu dalam menunjukkan indikasi adanya hidrokarbon pada reservoir. Atribut Dekomposisi Spektral yang didasari dari hasil komputasi CWT diharapkan dapat menjadi atribut yang berguna untuk mendeteksi adanya indikasi keberadaan hidrokarbon pada lapisan tipis. Untuk mendukung hasil metode CWT, akan dikombinasikan dengan hasil metode inversi untuk meyakinkan akan keberadaan hidrokarbon tersebut yang ditandai dengan nilai Elastic Impedance (EI) yang relatif rendah dengan sekitarnya.Dari hasil studi ini frekuensi dominan terlihat pada frekuensi 25 Hz, sedangkan pada frekuensi 10 Hz (frekuensi rendah) dan 30 Hz (frekuensi tinggi) anomali bright spot tidak terlihat di beberapa daerah prospek. Hal ini didukung dengan hasil inversi yang menunjukkan nilai EI yang rendah yaitu berkisar 13000 - 13750 ((ft/s) *(gr/cc)), 2370 - 2511((ft/s) *(gr/cc)), dan 600 - 620((ft/s) *(gr/cc)). Kombinasi metode dekomposisi spektral berbasis CWT dengan metode inversi seismik (EI) mengindikasikan adanya akumulasi gas pada beberapa daerah prospek.

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The Elastic Impedance inversion and the Spectral Decomposition process at the Penobscot field has been carried out, in order to identify the reservoir on a thin layer. The development of seismic attributes these days are very helpful in indicating any presence of Hydrocarbons in the reservoir. The Spectral Decomposition attribute, that based on the results of CWT computation is expected to become applicable in detecting and indicating any presence of Hydrocarbons in a thin layer. In order to support the results of CWT method, it will be combined with the one from the Inversion method, to assure the existence of such hydrocarbons which are characterized by the Elastic Impedance (EI) value that should be relatively low with its surroundings.

From the results of this study, the dominant frequency appears at 25 Hz, while in the frequency of 10 Hz (low frequency) and 30 Hz (high frequency), the bright spot anomaly has not been seen in some prospect areas. This result is supported by the inversion results that shows rather low EI values, ranged from 13000 to 13750 ((ft / s) * (g / cc)), from 2370 to 2511 ((ft / s) * (g / cc)), and from 600 to 620 ((ft / s) * (g / cc)). The combination of CWTbased spectral decomposition method with the seismic inversion methods (EI) indicates that there are an accumulation of gas in a some prospect areas."

"Lapangan Salemba dan Depok adalah lapangan gas yang berada di daerah Selat Madura. Pada dua sumur eksplorasi telah ditemukan akumulasi hidrokarbon gas pada Formasi Lidah yang berumur Plio-Pleistocene. Formasi Lidah didaerah studi ini diinterpretasikan sebagai sistem pengendapan channel. Permasalahan yang muncul dalam menganalisa data seismik untuk mengetahui geometri dari channel sendiri adalah adanya lapisan tipis yang tidak terdeteksi dan batas kontinuitas pelapisan yang kurang jelas. Oleh karena itu, diperlukan metode yang lebih baik untuk analisa data seismik agar masalah tersebut dapat diatasi.Dalam tesis ini, analisa data seismik metode dekomposisi spektral dengan algoritma Continuous Wavelet Transform (CWT) digunakan karena hasilnya dapat memberikan gambaran yang lebih baik dalam penyebaran ketebalan dan diskontinuitas geologi. Selain itu juga digunakan metode inversi seismik untuk mengetahui penyebaran impedansi akustik yang merupakan sifat fisis batuan.Hasil studi ini menunjukkan bahwa metode dekomposisi spektral dan inversi seismik telah berhasil membantu dalam mendeliniasi geometri channel Formasi Lidah. Penampang dekomposisi spektral merepresentasikan ketebalan dan diskontuniuitas geologi dari reservoir batupasir Formasi Lidah. Distribusi frekuensi pada reservoir direpresentasikan pada nilai frekuensi 10, 20, dan 30 Hz. Pada inversi seismik, penampang impedansi akustik merepresentasikan litologi bawah permukaan. Distribusi impedansi akustik pada reservoir mempunyai nilai rata-rata 15000 - 19700 ((ft/s)*(g/cc)), sedangkan pada non-reservoir mempunyai nilai impedansi akustik lebih dari 19700 ((ft/s)*(g/cc)).

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Salemba and Depok fields are a gas field which located in the Madura Strait. Two exploration wells have been discovered hydrocarbons accumulation of gas in the Lidah Formation aged Plio-Pleistocene. Lidah Formation in the study area was interpreted as channel depositional environment. The problem that then arises in analyzing seismic data to predict the channel geometry is undetected thin layer and unclear reservoir continuity. Therefore, the better method to analyze the seismic data is needed to solve the problem.

In this thesis, seismic data analysis spectral decomposition method with Continuous Wavelet Transform (CWT) is used because the results can provide a better map of the thickness distribution and geological discontinuities. This thesis is also used seismic inversion method to know the acoustic impedance distribution as the physical properties of rocks.

The result of this study shows that the spectral decomposition method and seismic inversion has helped to delineate the channel geometry of Lidah Formation. The section of spectral decomposition represents thickness and geological discontinuity in Lidah Formation. Frequency distribution in the reservoir has an average of 10, 20, and 30 Hz. In the seismic inversion, the section of acoustic impedance represents the subsurface lithology. Acoustic impedance distribution in the reservoir has an average of 15,000 - 19,700 ((ft/s)*(g/cc)), whereas in nonreservoir having an acoustic impedance more than 19,700 ((ft/s)*(g/cc))."

"A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis."