[
    {
        "id": "authors:qb77v-8wh17",
        "collection": "authors",
        "collection_id": "qb77v-8wh17",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170614-125957633",
        "type": "article",
        "title": "Trace formulas for Schr\u00f6dinger operators on star graphs",
        "author": [
            {
                "family_name": "Demirel-Frank",
                "given_name": "Semra",
                "clpid": "Demirel-Frank-S"
            },
            {
                "family_name": "Shou",
                "given_name": "Laura",
                "clpid": "Shou-Laura"
            }
        ],
        "abstract": "We derive trace formulas of the Buslaev\u2013Faddeev type for quantum star graphs. One of the new ingredients is high energy asymptotics of the perturbation determinant.",
        "doi": "10.1007/s13373-016-0097-y",
        "issn": "1664-3607",
        "publisher": "Springer",
        "publication": "Bulletin of Mathematical Sciences",
        "publication_date": "2018-04",
        "series_number": "1",
        "volume": "8",
        "issue": "1",
        "pages": "15-31"
    },
    {
        "id": "authors:jxgvy-0ra15",
        "collection": "authors",
        "collection_id": "jxgvy-0ra15",
        "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151222-103336784",
        "type": "book_section",
        "title": "Spectral Inequalities for Quantum Graphs",
        "book_title": "Mathematical Technology of Networks",
        "author": [
            {
                "family_name": "Demirel-Frank",
                "given_name": "Semra",
                "clpid": "Demirel-Frank-S"
            }
        ],
        "contributor": [
            {
                "family_name": "Mugnolo",
                "given_name": "Delio",
                "clpid": "Mugnolo-D"
            }
        ],
        "abstract": "We review our joint work with Evans Harrell on semiclassical and universal inequalities for quantum graphs. The proofs of these inequalities are based on an abstract trace inequality for commutators of operators. In this article we give a new proof of this abstract trace inequality. Another ingredient in proving semiclassical and universal inequalities is an appropriate choice of operators in this trace inequality. We provide a new approximation method for such a choice.",
        "doi": "10.1007/978-3-319-16619-3_6",
        "isbn": "978-3-319-16618-6",
        "publisher": "Springer",
        "place_of_publication": "Cham, Switzerland",
        "publication_date": "2015",
        "pages": "65-80"
    }
]